Question

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

(a) None

(b)

(c)

(d)

(e) None

(f) None

(g)

(h)

(i)

Step-by-step solution

Velocity

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

A cart moves to the left, gradually slowing down

(a)

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

A cart moves to the right, gradually speeding up

(b)

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

Hence the answer is graph number 6.

A cart moves to the left at a constant speed.

(c)

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

Hence the answer is graph number 3.

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 V_x is initially negative, then positive, and increasing.

Hence the answer is graph number 2.

 A cart remains stationary and does not move

(e)

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

 A cart moves to the right, gradually slowing down

(f)

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

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 V_x 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.

A cart moves to the left, gradually speeding up

(h)

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

Hence the answer is graph number 1.

 A cart moves to the right at a constant speed.

(i)

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

Hence the answer is graph number 4.