Question

A soccer ball slows down from 30.6 m/s, west ro limits , west during a 2.75seconds period. What is its average velocity? What is its average acceleration?

Answer 1

Given:

Initial velocity of the ball u = 30.6 m/s

Final velocity of the ball v = 0 m/s (rest)

Time taken t = 2.75 s

To find:

We have to find:

1) The average velocity $v_{avg}$

2) The average acceleration a

Solution:

1) The average velocity is given by the formula,

$v_{avg} = \frac{v\:+\:u}{2}$    

where v is the final velocity and u is the initial velocity.

Therefore, replacing the values of v and u in the above equation, we get,

⇒$v_{avg} = \frac{0\:+\:30.6}{2}$

∴$v_{avg} = 15.3m/s$

2) The acceleration is given by the formula,

$a=\frac{v\:-\:u}{t}$

where v is the final velocity, u is the initial velocity and t is the time taken.

⇒$a = \frac{0\:-\:30.6}{2.75}$

∴$a =-11.13m/s^{2}$

Here, the negative acceleration is also called deceleration.

The average velocity is $15.3$ m/s and the average acceleration is $-11.13$$m/s^{2}$ (deceleration).