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Chapter 2: Q. 7 (page 58)

FIGURE Q2.7 shows the position-versus-time graph for a moving

object. At which lettered point or points:

a. Is the object moving the fastest?

b. Is the object moving to the left?

c. Is the object speeding up?

d. Is the object turning around?

Short Answer

Expert verified

a. The object is moving the fastest from point C.

b. The object is moving to the left from point F.

c. The object is speeding up at point B.

d. The object is turning around from point E.

Step by step solution

01

Introduction

A graph showing an object at different position at different time is known as distance -time graph. The slope of this graph gives the value of speed . is moving such that at six different points the slope of position-time graph is different.

02

Explanation 

At point C, the slope of x-t graph is the steepest. So at point C the object is moving the fastest.

03

Part b; Step 1: Introduction

A tangent to the position-time curve of the given object determines its velocity.

04

Explanation

In the given graph, the slope of the curve at point F is negative. Which means, if we consider the positive x-axis as positive then at F , the object is moving in negative direction or towards the starting point.

So, from point F, the object is moving towards left.

05

Part c; Step 1: Introduction

The direction of the slope of velocity curve with positive x-axis determines whether the object is moving to the right of to the left.

06

Explanation

From point B, the slope of the curve is heading towards positive value or the magnitude of the slope is increasing. So from point B, the object is speeding up.

07

Part d; Step 1: Introduction

At point E the tangent to the x-t curve is parallel to positive x-axis.

08

Explanation

The slope of position-time curve is zero at point E. After this point , the slope is becoming negative . The curve is taking a turn round, reversing its direction of motion , from point E.

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Most popular questions from this chapter

Careful measurements have been made of Olympic sprinters

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

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鈥檚 run at the 1987

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

b = 0.6887 s-1.

a. What was Lewis鈥檚 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鈥檛 solve it for t. However, it鈥檚 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.

A rock is tossed straight up from ground level with a speed of 20 m/s. When it returns, it falls into a hole 10 m deep.
a. What is the rock鈥檚 velocity as it hits the bottom of the hole?
b. How long is the rock in the air, from the instant it is released until it hits the bottom of the hole?

A car starts from rest at a stop sign. It accelerates at 4.0 m/s2 for 6.0 s, coasts for 2.0 s, and then slows down at a rate of 3.0 m/s2 for the next stop sign. How far apart are the stop signs?

FIGURE EX2.32 shows the acceleration graph for a particle that starts from rest at t = 0 s. What is the particle鈥檚 velocity at t = 6 s?

The Starship Enterprise returns from warp drive to ordinary

space with a forward speed of 50 km/s. To the crew鈥檚 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鈥檚 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

鈥渂arely avoided鈥�? Once you decide what it looks like graphically,

express that situation mathematically.
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