Engineering Mechanics: Dynamics (14th Edition)
Engineering Mechanics: Dynamics (14th Edition)
14th Edition
ISBN: 9780133915389
Author: Russell C. Hibbeler
Publisher: PEARSON
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Chapter 12.6, Problem 3PP

Use the chain-rule and find ẏ and ӱ in terms of x, ẍ and x ⃛ if

a) y = 4x2

b) y = 3ex

c) y= 6 sin x

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Chapter 12 Solutions

Engineering Mechanics: Dynamics (14th Edition)

Ch. 12.2 - a. If s = (2t3) m, where t is in seconds,...Ch. 12.2 - Initially, the car travels along a straight road...Ch. 12.2 - Determine the time of flight when it returns to...Ch. 12.2 - A particle travels along a straight line with a...Ch. 12.2 - A particle travels along a straight line with a...Ch. 12.2 - Determine the time when the velocity of the...Ch. 12.2 - A particle travels along a straight line with an...Ch. 12.2 - A particle moves along a straight line such that...Ch. 12.2 - Determine the acceleration of the particle at s =...Ch. 12.2 - What is the particles velocity when t = 6 s, and...
Ch. 12.2 - If a particle has an initial velocity of v0 = 12...Ch. 12.2 - When t = 1 s, the particle is located 10m to the...Ch. 12.2 - When s =4ft, v = 3ft/s and when s = 10ft, v = 8...Ch. 12.2 - If s = 0 when t = 0, determine the particles...Ch. 12.2 - Determine the position of the particle when t = 6...Ch. 12.2 - Determine the average velocity, the average speed,...Ch. 12.2 - Determine (a) the displacement of the particle...Ch. 12.2 - If s = 1 m and v = 2 m/s when t = 0, determine the...Ch. 12.2 - Determine the particles velocity when s = 2 m, if...Ch. 12.2 - Then in another 5 s it moves from SB to SC = 6 m....Ch. 12.2 - How long will it take to reach a speed of 120...Ch. 12.2 - It takes about 3 s for a driver having 0.1%...Ch. 12.2 - Determine the total distance traveled when t = 10...Ch. 12.2 - If it is subjected to a deceleration of a = kv3,...Ch. 12.2 - Determine how far it travels before it stops. How...Ch. 12.2 - It takes the driver of car A 0.75 s to react (this...Ch. 12.2 - Determine the time needed for the rocket to reach...Ch. 12.2 - Afterwards it travels with a constant velocity for...Ch. 12.2 - If s = 4 ft when t = 0, determine the position of...Ch. 12.2 - Determine the distance traveled in three seconds,...Ch. 12.2 - If the bag is released with the same upward...Ch. 12.2 - If v = 20 m/s when s = 0 and t = 0, determine the...Ch. 12.2 - If v = 0, s = 1 m when t = 0, determine the...Ch. 12.2 - If the body is released from rest at a very high...Ch. 12.2 - At t 0,s 1 m and v = 10 m/s. When t 9 s,...Ch. 12.2 - Initially the particle falls from rest.Ch. 12.2 - Determine the distance between them when t = 4 s...Ch. 12.2 - Determine the height from the ground and the time...Ch. 12.2 - A sphere is fired downwards into a medium with an...Ch. 12.2 - If s = 0 when t = 0, determine the position and...Ch. 12.2 - Determine the elapsed time t 2v0/g from the...Ch. 12.2 - Neglecting air resistance, this acceleration is...Ch. 12.2 - Accounting for the variation of gravitational...Ch. 12.3 - Construct the v t graph for the same time...Ch. 12.3 - Construct the s t and a t graphs during the same...Ch. 12.3 - Construct the a s graph for the same interval.Ch. 12.3 - The sports car travels along a straight road such...Ch. 12.3 - Construct the v t graph for the time interval 0 ...Ch. 12.3 - Construct the s t graph during the time interval...Ch. 12.3 - A freight train starts from rest and travels with...Ch. 12.3 - The s-t graph for a train has been experimentally...Ch. 12.3 - Rocket A accelerates vertically at 20 m/s2 for 12...Ch. 12.3 - Construct the v-t and a-t graphs for the time...Ch. 12.3 - If the position of a particle is defined by s = [2...Ch. 12.3 - It then climbs in a straight line with a uniform...Ch. 12.3 - It can accelerate at 5 ft/s2 and then decelerate...Ch. 12.3 - Determine the total distance the car moves until...Ch. 12.3 - Determine the time t when the jet plane stops....Ch. 12.3 - The acceleration and deceleration that occur are...Ch. 12.3 - Draw the st and at graphs for the particle. When t...Ch. 12.3 - If the rocket starts at s = 0 when v = 0,...Ch. 12.3 - After 30 s the first stage, A, burns out and the...Ch. 12.3 - The flat part of the graph is caused by shifting...Ch. 12.3 - Determine the cars maximum velocity and the time t...Ch. 12.3 - Draw the v-s graph and determine the time needed...Ch. 12.3 - From the data, construct the s-t and a-t graphs...Ch. 12.3 - Determine the total distance the motorcycle...Ch. 12.3 - Determine the motorcycles acceleration and...Ch. 12.3 - Draw the s-t and a-t graphs. Also determine the...Ch. 12.3 - If it is subjected to the decelerations shown,...Ch. 12.3 - Determine the boats speed when s = 50 ft, 100 ft,...Ch. 12.3 - Construct the v-s graph.Ch. 12.3 - After 15 s the first stage A burns out and the...Ch. 12.3 - The speed of a train during the first minute has...Ch. 12.3 - If the elevator maintains a constant upward speed...Ch. 12.3 - Car A accelerates at 4 m/s2 for 10 s and then...Ch. 12.3 - If the position of a particle is defined as s =...Ch. 12.3 - Construct the st and at graphs for the motion....Ch. 12.3 - Draw the vs graph if v = 0 at s = 0.Ch. 12.3 - Determine the speed of the plane when it has...Ch. 12.3 - Construct the s-t and a-s graphs. Also, determine...Ch. 12.3 - Construct the a-s graph.Ch. 12.3 - Determine its acceleration when s = 100 m and when...Ch. 12.6 - Use the chain-rule and find and in terms of x, ...Ch. 12.6 - The particle travels from A to B. Identify the...Ch. 12.6 - The particle travels from A to B. Identify the...Ch. 12.6 - The particle travels from A to B. Identify the...Ch. 12.6 - If the x and y components of a particle's velocity...Ch. 12.6 - If its position along the x axis is x = (8t) m,...Ch. 12.6 - If x = (4t4) m, where t is in seconds, determine...Ch. 12.6 - A particle travels 3long a straight line path y =...Ch. 12.6 - If x = 8 m, vx = 8 m/s, and ax = 4 m/s2 when t = 2...Ch. 12.6 - If the box has x components of velocity and...Ch. 12.6 - Determine the maximum height h it reaches.Ch. 12.6 - The ball is kicked from point A with the initial...Ch. 12.6 - Determine the speed at which the basketball at A...Ch. 12.6 - Determine the range R.Ch. 12.6 - A ball is thrown from A. If it is required to...Ch. 12.6 - Determine the range R where it strikes the ground...Ch. 12.6 - If the velocity of a particle is defined as v(t) =...Ch. 12.6 - If r = 0 when t = 0, determine the displacement of...Ch. 12.6 - Determine the particles position (x, y, z) at t =...Ch. 12.6 - If the particle is at the origin when t = 0,...Ch. 12.6 - Determine the point B(x, y) where the water...Ch. 12.6 - Determine the particles position (x, y, z) when t...Ch. 12.6 - It takes 4 s for it to go from B to C and then 3 s...Ch. 12.6 - It takes 8 s for it to go from B to C and then 10...Ch. 12.6 - Determine the magnitude of the crates velocity and...Ch. 12.6 - If the x component of acceleration is...Ch. 12.6 - If the component of velocity along the x axis is...Ch. 12.6 - Determine the x and y components of its velocity...Ch. 12.6 - If it takes 3 s for it to go from A to C,...Ch. 12.6 - Determine the magnitudes of its velocity and...Ch. 12.6 - If the link moves with a constant speed of 10 m/s,...Ch. 12.6 - If it has a constant speed of 75 ft/s, determine...Ch. 12.6 - Determine the distance the helicopter is from...Ch. 12.6 - Determine the minimum initial velocity v0 and the...Ch. 12.6 - If it takes 1.5 s to travel from A to B, determine...Ch. 12.6 - Neglecting the size of the ball, determine the...Ch. 12.6 - The girl at A can throw a ball at vA = 10 m/s....Ch. 12.6 - If vA = 10 m/s, determine the range R if this...Ch. 12.6 - Determine the point (x, y) where it strikes the...Ch. 12.6 - If it strikes the ground at B having coordinates x...Ch. 12.6 - Determine the distance d to where it will land.Ch. 12.6 - Determine the speed at which it strikes the ground...Ch. 12.6 - Neglecting the size of the ball, determine the...Ch. 12.6 - If he strikes the ground at B, determine his...Ch. 12.6 - If he strikes the ground at B, determine his...Ch. 12.6 - Determine the horizontal velocity vA of a tennis...Ch. 12.6 - If the acceleration varies with time as shown,...Ch. 12.6 - Determine the range R, the maximum height h...Ch. 12.6 - Determine the maximum and minimum speed at which...Ch. 12.6 - Also, what is the corresponding angle A at which...Ch. 12.6 - Also, what is the corresponding angle A at which...Ch. 12.6 - Note that the first dart must be thrown at C( D)...Ch. 12.6 - Determine the time for a particle of water leaving...Ch. 12.6 - The snowmobile is traveling at 10 m/s when it...Ch. 12.6 - Water flows from the hose at vA = 80 ft/s.Ch. 12.6 - When the ball is directly overhead of player B he...Ch. 12.6 - If it takes 1.5 s to travel from A to B, determine...Ch. 12.7 - a. Determine the acceleration at the instant...Ch. 12.7 - Determine the magnitude of its acceleration when t...Ch. 12.7 - Determine the magnitude of its acceleration when s...Ch. 12.7 - If the car decelerates uniformly along the curved...Ch. 12.7 - Determine the direction of the crates velocity,...Ch. 12.7 - If the motorcycle has a deceleration of at =...Ch. 12.7 - The car travels up the hill with a speed of v =...Ch. 12.7 - If the acceleration of the automobile is 5 ft/s2,...Ch. 12.7 - Determine the maximum constant speed a race car...Ch. 12.7 - If it then increases its speed along a circular...Ch. 12.7 - Determine the speed of the particle and its normal...Ch. 12.7 - Determine the radius of curvature of the path at...Ch. 12.7 - If its speed is increased by v = (0.05t2) ft/s2,...Ch. 12.7 - If it then starts to increase its speed at v =...Ch. 12.7 - If they are at the positions shown when t = 0,...Ch. 12.7 - At the instant shown, A has a speed of 60ft/sand...Ch. 12.7 - If the acceleration is 2.5 m/s2, determine the...Ch. 12.7 - Determine the magnitudes of its velocity and...Ch. 12.7 - Determine the magnitude of the cars acceleration...Ch. 12.7 - If the car passes point A with a speed of 20m/s...Ch. 12.7 - The motorcycle is traveling at 1 m/s when it is at...Ch. 12.7 - Determine the magnitude of the acceleration of the...Ch. 12.7 - Determine the magnitudes of its velocity and...Ch. 12.7 - Determine the magnitudes of its velocity and...Ch. 12.7 - Determine the rate of increase in the train's...Ch. 12.7 - If it increases its speed along the circular track...Ch. 12.7 - Determine the time when the magnitude of...Ch. 12.7 - If its speed at t = 0 is 15 ft/s and is increasing...Ch. 12.7 - Determine the magnitude of the boat's acceleration...Ch. 12.7 - Determine the magnitudes of his velocity and...Ch. 12.7 - If it is initially traveling with a speed of 10...Ch. 12.7 - Determine the magnitude of its acceleration when...Ch. 12.7 - Determine the magnitude of the acceleration of the...Ch. 12.7 - Determine the rate of increase in the planes...Ch. 12.7 - Find the equation of the path, y = f (x), and then...Ch. 12.7 - The motorcycle is traveling at 40 m/s when it is...Ch. 12.7 - If the speed limit is posted at 60 km/h, determine...Ch. 12.7 - Prob. 140PCh. 12.7 - Determine the normal and tangential components of...Ch. 12.7 - Take =150 m.Ch. 12.7 - The motorcycle travels along the elliptical track...Ch. 12.7 - The motorcycle travels along the elliptical track...Ch. 12.7 - If at the instant shown the speed of A begins to...Ch. 12.7 - If the speed of B is increasing by (at)B = 4m/s2,...Ch. 12.7 - Also, specify the direction of flight, measured...Ch. 12.7 - Determine the magnitude of the acceleration of the...Ch. 12.7 - The train passes point B with a speed of 20 m/s...Ch. 12.7 - Determine the magnitude of the acceleration of the...Ch. 12.7 - Determine the particles acceleration when it is...Ch. 12.7 - When t = 8 s, determine the coordinate direction...Ch. 12.7 - Prob. 153PCh. 12.7 - If the speed of the crate at A is 15 ft/s, which...Ch. 12.8 - Determine the angular velocity of the radial line...Ch. 12.8 - A ball rolls outward along the radial groove so...Ch. 12.8 - Peg P is driven by the fork link OA along the...Ch. 12.8 - Peg P is driven by the forked link OA along the...Ch. 12.8 - Determine the magnitude of the velocity of the...Ch. 12.8 - At the instant = 45, the athlete is running with...Ch. 12.8 - A particle is moving along a circular path having...Ch. 12.8 - Determine the radial and transverse components of...Ch. 12.8 - Determine the components of its velocity and...Ch. 12.8 - If the propeller has a diameter of 6 ft and is...Ch. 12.8 - Express the velocity and acceleration of the...Ch. 12.8 - Determine the magnitudes of velocity and...Ch. 12.8 - If a particle moves along a path such that r = (2...Ch. 12.8 - If a particle moves along a path such that r =...Ch. 12.8 - At the instant shown, its angular rate of rotation...Ch. 12.8 - Determine the angular rate of rotation of the...Ch. 12.8 - Calculate this vector, a, in terms of its...Ch. 12.8 - such that its position as a function of time is...Ch. 12.8 - Determine the radial and transverse components of...Ch. 12.8 - Determine the magnitudes of the velocity and...Ch. 12.8 - Determine the velocity and acceleration of the...Ch. 12.8 - Determine the radial and transverse components of...Ch. 12.8 - If it is assumed that the hose lies in a...Ch. 12.8 - Two pin-connected slider blocks, located at B....Ch. 12.8 - Determine the magnitude of the acceleration of the...Ch. 12.8 - If the geometry of the fixed rod for a short...Ch. 12.8 - The platform rotates at a constant rate of 6...Ch. 12.8 - Determine the cars radial and transverse...Ch. 12.8 - Determine the cars radial and transverse...Ch. 12.8 - If it maintains a constant speed of v = 35 ft/s,...Ch. 12.8 - Determine the cylindrical components of the...Ch. 12.8 - Determine the maximum and minimum magnitudes of...Ch. 12.8 - The peg is constrained to move in the slots of the...Ch. 12.8 - When = 30, the angular velocity and angular...Ch. 12.8 - Determine the angular rate of rotation of the...Ch. 12.8 - A truck is traveling along the horizontal circular...Ch. 12.8 - Two pin-connected slider blocks, located at B,...Ch. 12.8 - Determine the magnitude of the acceleration of the...Ch. 12.8 - The searchlight on the boat anchored 2000 ft from...Ch. 12.8 - If the car in Prob.12-187 is accelerating at 15...Ch. 12.8 - If = 4 rad/s (constant), determine the radial and...Ch. 12.8 - if the particle has an angular acceleration = 5...Ch. 12.8 - If = (0.5t)rad, where t is in seconds, determine...Ch. 12.8 - Determine the magnitudes of the velocity and...Ch. 12.8 - When t = 0, = 0. Use Simpson's rule with n = 50...Ch. 12.8 - The double collar C is pin connected together such...Ch. 12.10 - Determine the velocity of block D if end A of the...Ch. 12.10 - Determine the velocity of block A if end B of the...Ch. 12.10 - Determine the velocity of block A if end B of the...Ch. 12.10 - Determine the velocity of block A if end F of the...Ch. 12.10 - Determine the velocity of car A if point P on the...Ch. 12.10 - Determine the velocity of cylinder B if cylinder A...Ch. 12.10 - Determine the velocity of car B relative to car A.Ch. 12.10 - Determine the magnitude and direction of the...Ch. 12.10 - Determine the distance between them when t = 4 s.Ch. 12.10 - If B is accelerating at 1200 km/h2 while A...Ch. 12.10 - If the end of the cable at A is pulled down with a...Ch. 12.10 - The motor at D draws in its cable at aD = 5 m/s2....Ch. 12.10 - If BC remains fixed while the plunger P is pushed...Ch. 12.10 - If the end of the cable at A is pulled down with a...Ch. 12.10 - Determine the displacement of the log if the truck...Ch. 12.10 - Determine the constant speed at which the cable at...Ch. 12.10 - Determine the time needed to lift the load 7 m.Ch. 12.10 - If the end A of the cable is moving at vA = 3 m/s,...Ch. 12.10 - Determine the time needed for the load at B to...Ch. 12.10 - Determine the velocity of the block.Ch. 12.10 - If block A of the pulley system is moving downward...Ch. 12.10 - Determine the speed of the block at B.Ch. 12.10 - Determine the speed of block A if the end of the...Ch. 12.10 - The motor draws in the cable at D with a constant...Ch. 12.10 - The pulley at A is attached to the smooth collar...Ch. 12.10 - When sB = 6ft. the end of the cord at B is pulled...Ch. 12.10 - Determine the velocity and acceleration of block B...Ch. 12.10 - Determine how fast the boat approaches the pier at...Ch. 12.10 - If the hydraulic cylinder H draws in rod BC at 2...Ch. 12.10 - The car at B is traveling at 18.5 m/s along the...Ch. 12.10 - When sA = 1.5 m, vB = 6 m/s. Determine the...Ch. 12.10 - If block B is moving down with a velocity vB and...Ch. 12.10 - Determine the velocity and acceleration of the...Ch. 12.10 - If their velocities are vA = 500km/h and vB =...Ch. 12.10 - If B is increasing its speed by 1200mi/h2, while A...Ch. 12.10 - The point of destination is located along the...Ch. 12.10 - If vA = 40ft/s and vB = 30 ft/s. determine the...Ch. 12.10 - An instrument in the car indicates that the wind...Ch. 12.10 - If vA = 10m/s and vB = 15m/s, determine the...Ch. 12.10 - At the same instant, car B is decelerating at 250...Ch. 12.10 - At the instant shown, A has a speed of 90ft/sand...Ch. 12.10 - If raindrops fall vertically at 7 km/h in still...Ch. 12.10 - If B is increasing its velocity by 2 m/s2, while A...Ch. 12.10 - If A is increasing its speed at 4 m/s2, whereas...Ch. 12.10 - Compute the terminal (constant) velocity vr of the...Ch. 12.10 - He wishes to cross the 40-ft-wide river to point...Ch. 12.10 - Determine the magnitude and direction of the...Ch. 12.10 - At the instant the ball is thrown, the player is...Ch. 12.10 - At the instant the ball is thrown, the player is...Ch. 12.10 - Determine the constant speed at which the player...Ch. 12.10 - At this same instant car B travels along the...Ch. 12.10 - If you measured the time it takes for the...Ch. 12.10 - Determine its maximum acceleration and maximum...Ch. 12.10 - Originally s0 = 0.Ch. 12.10 - A projectile, initially at the origin, moves along...Ch. 12.10 - Determine the acceleration when t = 2.5 s, 10 s,...Ch. 12.10 - If it takes 3 s to go from A to B, and then 5 s to...Ch. 12.10 - From a videotape, it was observed that a player...Ch. 12.10 - The truck travels in a circular path having a...Ch. 12.10 - If the car starts from rest when = 0, determine...Ch. 12.10 - Determine the magnitude of the particles...Ch. 12.10 - Determine the time needed for the load at B to...Ch. 12.10 - If their velocities are vA = 600 km/h and vB = 500...

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