Question

Questions & Problems1. Kinematics Problem: A ball initially at rest rolls down a hill and accelerates at a rate of 3.0m/s?. After 12 seconds find....• The velocity of the ball.The distance travelled by the ball.

Answer 1

Since the acceleration is constant this is a uniform accelerated motion.

We know that the acceleration is 3 meters per second per second and that the initial velocity is zero (since it starts at rest).

To find the velocity after 12 seconds we use the formula:

`a=(v_f-v_0)/(t)`

plugging the values given ans solvin for the final velocity we have:

`\begin{gathered} 3=(v_f-0)/(12)_{} \\ v_f=3(12) \\ v_f=36 \end{gathered}`

Therefore after 12 seconds the ball has a velocity of 36 m/s.

Now, to find the distance travelled we use the formula:

`d=v_0t+(1)/(2)at^2`

Plugging the values we know we have that:

`\begin{gathered} d=(0)(12)+(1)/(2)(3)(12)^2 \\ d=216 \end{gathered}`

Therefore the ball travelled 216 meters.