# What is the average speed of an object that is still at t=0 and accelerates at a rate of a(t) = 5t from t in [0,1]?

Mar 25, 2017

The average speed is $= 2.5 m {s}^{-} 1$

#### Explanation:

The acceleration is

$a \left(t\right) = 5 t$

The speed is the integral of the acceleration

$v \left(t\right) = \int a \left(t\right) \mathrm{dt}$

Let the average speed be $\overline{v}$

Then,

$\left(1 - 0\right) \overline{v} = {\int}_{0}^{1} 5 t \mathrm{dt} = {\left[\frac{5}{2} {t}^{2}\right]}_{0}^{1}$

$\overline{v} = \frac{5}{2} = 2.5 m {s}^{-} 1$