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:

$a=\frac{v_f-v_0}{t}$

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

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

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

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

$d=v_0t+\frac{1}{2}at^2$

Plugging the values we know we have that:

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

Therefore the ball travelled 216 meters.