Question

A ball accelerates uniformly at +4.0m/s^2. If the ball was initially moving at +0.20m/s and the average velocity was +4.2 m/s, then how long will it take to reach the final velocity? Please show how you get this. I am sooo lost. I want to learn how, not just get the answer. Thank you!

Answer 1

Let's use two SUVAT equations:
http://en.wikipedia.org/wiki/Equations_of_motion#SUVAT_equations

We know that the average velocity is \(\cfrac{u+v}{2}\), where \(u\) is in the initial velocity and \(v\) is the final velocity. This is equal to 4.2 m/s, a given.

First SUVAT equation we will use:
$$
s=\cfrac{(u+v)t}{2}=4.2~t
$$
Where, s is the distance traveled and t is the time to reach the average velocity of 4.2 m/s.

Second SUVAT equation we will use:
$$
s=ut+\cfrac{at^2}{2}
$$
Where \(a\) is the acceleration, \(4.2~m/s^2\), a given.

Equate these two equations and solve for t:
$$
ut+\cfrac{at^2}{2}=4.2~t\\
0.2t+\cfrac{4.2t^2}{2}=4.2~t
$$

Solving for t, I get 2.26 seconds.