Chapter 12, Problem 68P

For 10 seconds, a race automobile accelerates at a = 5 + 2t m/s2 after starting from a rest. The brakes are then applied and the car has constant acceleration of a=-30m/s2 until it come to rest. Calculate the total travel time.

A roller coaster starts from rest at A, rolls down the track to B, describes a circular loop of 40-ft diameter, and moves up and down past Point E. Take h=74 ft and assume that there is no energy loss due to friction. D = 20 ft C B Determine the force exerted by his seat on a 195-lb rider at B and D. lb. ↑ The force exerted by seat on the rider at Bis The force exerted by seat on the rider at Dis lb. ↓

The 13.3-in. spring is compressed to a 6.9-in. length, where it is released from rest and accelerates the sliding block A. The acceleration has an initial value of 280 ft/sec² and then decreases linearly with the x-movement of the block, reaching zero when the spring regains its original 13.3-in. length. Calculate the time t for the block to go (a) 3.2 in. and (b) 6.4 in. -6.9" -13.3" Answers: To go 3.2 in., t= To go 6.4 in., t = i sec sec

A particle moving in the x-y plane has a position vector given by r = 3/2t² i + 2/3t³j, where r is in inches and t is in seconds. Calculate the radius of curvature p of the path for the position of the particle when t = 2.0 sec. Sketch the velocity v and the curvature of the path for this particular instant. Answer: p= i in.

At time t = 0, a particle is at rest in the x-y plane at the coordinates (xo, Yo) = (8,0) in. If the particle is then subjected to the acceleration components ax = 0.53 -0.27t in./sec² and ay = 0.13t-0.04t2 in. /sec², determine the coordinates of the particle position when t = 6 sec. You might consider plotting the path of the particle during this time period. Answer: (x, y) = (i -11.62 -245.16 )in.

At time t = 0, a particle is at rest in the x-y plane at the coordinates (xo, Yo) = (8, 0) in. If the particle is then subjected to the acceleration components ax=0.53 -0.27t in./sec² and ay = 0.13t - 0.04t² in./sec², determine the coordinates of the particle position when t = 6 sec. You might consider plotting the path of the particle during this time period. Answer: (x, y) = (7.82 -0.3715 )in.

write the detail solution please

4. A car starts from rest and accelerates uniformly to a speed of 72 km/h. over a distance of 500 m. Calculate the acceleration and the time taken to attain the speed. If a further acceleration raises the speed to 90 km/h in 10 seconds, find this acceleration and the further distance moved. The brakes are now applied to bring the car to rest under uniform retardation in 5 seconds. Find the distance travelled during braking.

1. Draw a FBD of the skier during the lifting process. Ensure you include all forces and a coordinate system. 2. Obtain the equation of motion of the skier as a function of the only unknowns x (and/or its derivatives) and T (ie express all other quantities numerically). 3. The skier starts their journey up the ski lift at t = 0, and they reach the top of the slope at tend=224 s. The skier’s position, x, as a function of time, t, over this time period is given by:   Obtain the analytical expression of the tension with respect to time and compute the maximum tension value. Note: The coordinate x is parallel to the slope (in the same direction as the motion of the skier) as marked in the diagram above.