Question

A ball is rolled at an initial speed of 5 m/s and finishes a certain distance at a speed of 7 m/s. if the ball rolled for 9 seconds then how long was this distance that the ball rolled?

Answer 1

Answer:

The ball rolled a distance of 54 m.

Explanation:

Given:

Initial velocity of the ball is, $u=5\ m/s$

Final velocity of the ball is, $v=7\ m/s$

Time for rolling is, $t=9\ s$

The distance of rolling is, $S=?$

First, let us find the acceleration of the ball using Newton's equation of motion as:

$v=u+at\\a=\frac{v-u}{t}\\a=\frac{7-5}{9}=\frac{2}{9}\ m/s^2$

Now, displacement of the ball can be determined using the following equation of motion:

$v^2=u^2+2aS$

Rewriting the above in terms of 'S', we get

$S=\frac{v^2-u^2}{2a}$

Plug in the known values and solve for 'S'. This gives,

$S=\frac{7^2-5^2}{2\times \frac{2}{9}}\\\\S=\frac{49-25}{\frac{4}{9}}\\\\S=\frac{9\times 24}{4}\\\\S=9\times 6=54\ m$

Therefore, the ball rolled a distance of 54 m.