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Chapter 2: Q. 4 (page 58)

FIGURE Q2.4 shows a position-versus-time graph for the motion of

objects A and B as they move along the same axis.

a. At the instant t = 1 s, is the speed of A greater than, less than,

or equal to the speed of B? Explain.

b. Do objects A and B ever have the same speed? If so, at what

time or times? Explain.

Short Answer

Expert verified

(a) The speed of particle A is less than the speed of particle B.

(b) The speed of both of the particles A and B become the same in time3s.

Step by step solution

01

Part (a) Step 1: Introduction

Two objects, A and B are moving along same axis. We have to compare the speed of the two.

02

Explanation

At the instant t=1sec, considering the position of the particles A and B by the following graph:


Clearly, at t=1s, particle B covers more distance than particle A.

Therefore, speed of B is greater than A at that time as the speed changes proportionally with distance.

03

Part (b): Step 1: Given information

The position-time graphs of particle A and B intersect at a point.

04

Explanation

The path of motion of the two particles A and B intersects at a point. So, the speed of both of the particles should be same at that instantaneous time as shown in the graph:

05

Final answer

Therefore, at timet=3s, both of the particles A and B have the same speed.

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Most popular questions from this chapter

The Starship Enterprise returns from warp drive to ordinary

space with a forward speed of 50 km/s. To the crew’s great surprise,

a Klingon ship is 100 km directly ahead, traveling in the

same direction at a mere 20 km/s. Without evasive action, the

Enterprise will overtake and collide with the Klingons in just

slightly over 3.0 s. The Enterprise’s computers react instantly to

brake the ship. What magnitude acceleration does the Enterprise

need to just barely avoid a collision with the Klingon ship?

Assume the acceleration is constant.

Hint: Draw a position-versus-time graph showing the motions

of both the Enterprise and the Klingon ship. Let x0 = 0 km be

the location of the Enterprise as it returns from warp drive. How

do you show graphically the situation in which the collision is

“barely avoided”? Once you decide what it looks like graphically,

express that situation mathematically.

Careful measurements have been made of Olympic sprinters

in the 100 meter dash. A quite realistic model is that the sprinter’s

velocity is given by

vx=a(1-e-bt)

where t is in s, vx is in m/s, and the constants a and b are characteristic

of the sprinter. Sprinter Carl Lewis’s run at the 1987

World Championships is modeled with a = 11.81 m/s and

b = 0.6887 s-1.

a. What was Lewis’s acceleration at t = 0 s, 2.00 s, and 4.00 s?

b. Find an expression for the distance traveled at time t.

c. Your expression from part b is a transcendental equation,

meaning that you can’t solve it for t. However, it’s not hard to

use trial and error to find the time needed to travel a specific

distance. To the nearest 0.01 s, find the time Lewis needed to

sprint 100.0 m. His official time was 0.01 s more than your

answer, showing that this model is very good, but not perfect.

In the problem, you are given the kinematic equation that are used to solve a problem.

  1. Write a realistic problem for which this is the correct equation. Be sure that the answer your problem requests is consistent with the equation given.
  2. Draw the pictorial presentation for your problem.
  3. Finish the solution of the problem.

64m=0m+32m/s4s-0s+12ax4s-0s2

Larry leaves home at 9:05 and runs at a constant speed to the lamp post seen in FIGURE EX2.3. He reaches the lamppost at 9:07, immediately turns, and runs to the tree. Larry arrives at the tree at 9:10. a. What is Larry’s average velocity, in m/min, during each of these two intervals? b. What is Larry’s average velocity for the entire run?

A rock is thrown (not dropped) straight down from a bridge into the

river below. At each of the following instants, is the magnitude of the rock’s acceleration greater than g, equal to g, less than g, or 0? Explain.

a. Immediately after being released.

b. Just before hitting the water.
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