•16 The position function x(t) of a particle moving along an x axisis x = 4.0 – 6.01², with x in meters and t in seconds. (a) At whattime and (b) where does the particle (momentarily) stop? At what(c) negative time and (d) positive time does the particle passthrough the origin? (e) Graph x versus t for the range -5 s to +5 s.(f) To shift the curve rightward on the graph, should we include theterm +201 or the term -201 in x(t)? (g) Does that inclusion in-crease or decrease the value ofx at which the particle momentarilystops?

As per guidelines, the first four sub-parts have been answered.

Answered: •16 The position function x(t) of a…

Principles of Physics: A Calculus-Based Text

5th Edition

ISBN:9781133104261

Author:Raymond A. Serway, John W. Jewett

Publisher:Raymond A. Serway, John W. Jewett

Chapter3: Motion In Two Dimensions

Section: Chapter Questions

Problem 3CQ

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A projectile is launched from the point (x = 0, y = 0), with velocity (12.0i19.0j)m/s2, at t = 0. (a) Make a table listing the projectiles distance r from the origin at the end of each second thereafter, for 0 t 10 s. Tabulating the x and y coordinates and the components of velocity vx and vy will also be useful. (b) Notice that the projectiles distance from its starting point increases with time, goes through a maximum, and starts to decrease. Prove that the distance is a maximum when the position vector is perpendicular to the velocity. Suggestion: Argue that if v is not perpendicular to r, then r must lie increasing or decreasing. (c) Determine the magnitude of the maximum displacement. (d) Explain your method for solving part (c).
A celebrated Mark Twain story has motivated contestants in the Calaveras County Jumping Frog Jubilee, where frog jumps as long as 2.2 m have been recorded. If a frog jumps 2.2 m and the launch angle is 45, find (a) the frogs launch speed and (b) the time the frog spends in the air. Ignore air resistance.
A blue car of length 4.52 m is moving north on a roadway (hat intersects another perpendicular roadway (Fig. P2.81, page 58). The width of the intersection from near edge to far edge is 28.0 m. The blue car has a constant acceleration of magnitude 2.10 m/s2 directed south. The time interval required for the nose of the blue car to move from the near (south) edge of the intersection to the north edge of the intersection is 3.10 s. (a) How far is the nose of the blue car from the south edge of the intersection when it stops? (b) For what time interval is any part of the blue car within the boundaries of the intersection? (c) A red car is at rest on the perpendicular intersecting roadway. As the nose of the blue car enters the intersection, the red car starts from rest and accelerates east at 5.60 m/s2. What is the minimum distance from the near (west) edge of the intersection at which the nose of the red car can begin its motion if it is to enter the intersection alter the blue car has entirely left the intersection? (d) II the red car begins its motion at the position given by the answer to pan (c), with what speed does it enter the intersection?
A pirate has buried his treasure on an island with five trees located at the points (30.0 m, 20.0 m), (60.0 m, 80.0 m). (10.0 m, 10.0 m), (40.0 m, 30.0 m), and (70.0 m, 60.0 m), all measured relative to some origin, as shown in Figure P3.46. His ships log instructs you to start at tree A and move toward tree B, but to cover only one-half the distance between A and B. Then move toward tree C, covering one-third the distance between your current location and C. Next move toward tree D, covering one-fourth the distance between where you are and D. Finally move toward tree E, covering one-fifth the distance between you and E, stop, and dig. (a) Assume you have correctly determined the order in which the pirate labeled the trees as A, B, C, D, and E as shown in the figure. What are the coordinates of the point where his treasure is buried? (b) What If? What if you do not really know the way the pirate labeled the trees? What would happen to the answer if you rearranged the order of the trees, for instance, to B (30 m, 20 m), A (60 m, 80 m), E (10 m, 10 m), C (40 m, 30 m), and D (70 m, 60 m)? State reasoning to show that the answer does not depend on the order in which the trees are labeled. Figure P3.46
In the particle under constant acceleration model, we identify the variables and parameters vxi, vxf, ax, t, and xf xi. Of the equations in Table 2.2, the first does not involve xf xi, the second does not contain ax, the third omits vxf, and the last leaves out t. So, to complete the set, there should be an equation not involving vxi. (a) Derive it from the others. (b) Use the equation in part (a) to solve Problem 23 in one step.
After a ball rolls off the edge of a horizontal table at time t = 0, its velocity as a function of time is given by v=1.2i9.8tj where v is in meters per second and t is in seconds. The balls displacement away from the edge of the table, during the time interval of 0.380 s for which the ball is in flight, is given by r=00.3803vdt To perform the integral, you can use the calculus theorem [A+Bf(x)]dx=Adx+Bf(x)dx You can think of the units and unit vectors as constants, represented by A and B. Perform the integration to calculate the displacement of the ball from the edge of the table at 0.380 s.
(a) Repeat the problem two problems prior, but for the second leg you walk 20.0 m in a direction 40.0° north of east (which is equivalent to subtracting B from A that is, to finding R=AB ). (b) Repeat the problem two problems prior, but now you first walk 20.0 m in a direction 40.0° south of west and then 12.0 m in a direction 20.0° east of south (which is equivalent to subtracting A from B that is, to finding R=BA=R ). Show that this is the case.
Find the following for path A in Figure 3.54: (a) the total distance traveled, and (b) the magnitude and direction of the displacement from start to finish.
As she picks up her riders, a bus driver traverses four successive displacements represented by the expression (6.30 b)i (4.00 b cos 40)i (4.00 b sin 40)j + (3.00 b cos 50)i (3.00 b sin 50)j (5.00 b)j Here b represents one city block, a convenient unit of distance of uniform size; i is east; and j is north. The displacements at 40 and 50 represent travel on roadways in the city that are at these angles to the main east-west and north-south streets, (a) Draw a map of the successive displacements, (b) What total distance did she travel? (c) Compute the magnitude and direction of her total displacement. The logical structure of this problem and of several problems in later chapters was suggested by Alan Van Heuvelen and David Maloney, American Journal of Physics 67(3) 252-256, March 1999.
Consider the following combinations of signs and values for the velocity and acceleration of a particle with respect to a one-dimensional x-axis: Velocity Acceleration a. Positive Positive b. Positive Negative c. Positive Zero d. Negative Positive e. Negative Negative f. Negative Zero g. Zero Positive h. Zero Negative Describe what the particle is doing in each case and give a real-life example for an automobile on an east-west one-dimensional axis, with east considered the positive direction.
A daring ranch hand sitting on a tree limb wishes to drop vertically onto a horse galloping under the tree. The constant speed of the horse is 10.0 m/s, and the distance from the limb to the level of the saddle is 3.00 m. (a) What must be the horizontal distance between the saddle and limb when the ranch hand makes his move? (b) For what time interval is he in the air?
The position of a particle moving along the x -axis varies with time according to x(t)=5.0t24.0t3 . Find (a) the velocity and acceleration of the particle as functions of time, (b) the velocity and acceleration at t=2.0s , (c) the time at which the position is a maximum, (d) the time at which the velocity Is zero, and (e) the maximum position.

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