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Chapter 2: Q29P (page 84)

For each graph of vx vs. t numbered 1-6 in Figure, choose the letter (a-i) corresponding to the appropriate description of motion of a fan cart moving along a track. Not all descriptions will be used. Assume the usual coordinate system (+x to the right, +y up. +z out of the page).

(a) A cart moves to the left, gradually slowing down.

(b) A cart moves to the right, gradually speeding up.

(c) A cart moves to the left at a constant speed.

(d) A cart moves to the left, gradually slowing down, stops, and moves to the right, speeding up.

(e) A cart remains stationary and does not move.

(f) A cart moves to the right, gradually slowing down,

(g) A cart moves to the right. gradually slowing down, stops, and moves to the left, speeding up.

(h) A cart moves to the left, gradually speeding up.

(i) A cart moves to the right at a constant speed.

Short Answer

Expert verified

(a) None

(b)

(c)

(d)

(e) None

(f) None

(g)

(h)

(i)

Step by step solution

01

Velocity

The rate at which displacement changes with respect to time is known as velocity. Same as displacement velocity is also a vector quantity.

02

A cart moves to the left, gradually slowing down

(a)

There is no graph that matches this type of description of motion.

03

A cart moves to the right, gradually speeding up

(b)

This description matches this graph in which Vx is positive and increasing.

Hence the answer is graph number 6.

04

A cart moves to the left at a constant speed.

(c)

This description matches this graph in which Vx is negative and constant.

Hence the answer is graph number 3.

05

A cart moves to the left, gradually slowing down, stops, and moves to the right, speeding up

(d)

This description matches this graph in which Vx is initially negative, then positive, and increasing.

Hence the answer is graph number 2.

06

 A cart remains stationary and does not move

(e)

There is no graph that matches this type of description of motion

07

 A cart moves to the right, gradually slowing down

(f)

There is no graph that matches this type of description of motion.

08

A cart moves to the right. Gradually slowing down, stops, and moves to the left, speeding up

(g)

This description matches this graph in which Vx is initially positive and then negative and decreasing, and at a point, it is zero, then again increasing.

Hence the answer is graph number 5.

09

A cart moves to the left, gradually speeding up

(h)

This description matches this graph in which Vx is negative and increasing.

Hence the answer is graph number 1.

10

 A cart moves to the right at a constant speed.

(i)

This description matches this graph in which Vx is positive and constant.

Hence the answer is graph number 4.

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