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.

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

(a)

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

(b)

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

Hence the answer is graph number 6.

(c)

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

Hence the answer is graph number 3.

(d)

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

Hence the answer is graph number 2.

(e)

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

(f)

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

(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.

(h)

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

Hence the answer is graph number 1.

(i)

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

Hence the answer is graph number 4.