Question

A small cart is rolling freely on an inclined ramp with a constant acceleration of 0.50 m/s^2 in the - (negative) x direction. At time t = 0, the cart has a velocity of 2.0 m/s in the + (positive) x-direction. If the cart never leaves the ramp, which of the following statements correctly describes the motion of the cart at a time t > 5 s?

A. The cart is traveling in the +x-direction and is slowing down.
B. The cart is traveling in the +x-direction and is speeding up.
C. The cart is traveling in the –x-direction and is speeding up.
D. The cart is traveling in the –x-direction and is slowing down.

A ball is thrown with an initial speed of 20 m/s at an angle of 60° to the ground. If air resistance is negligible, what is the ball’s speed at the instant it reaches its maximum height from the ground?

A. - 20 m/s
B. 0 m/s
C. + 17.3 m/s
D. + 10 m/s
E. + 20 m/s

Answer 1

First problem

Calculate at what time the cart will stop due to gravity:

$$t=(v_f-v_i)/a=(0-2)/(-0.5)=4\text{ s}.$$

Therefore, at time t>5 seconds the cart is traveling in the –x-direction and is speeding up.

Second problem

At the point of maximum height ball's vertical component of velocity is 0. Therefore, it has only horizontal component. If the ball was shot in the positive x direction, its speed will be +20 m/s since there are no forces that can affect the horizontal component of velocity.