What is the average speed of an object that is not moving at t=0 and accelerates at a rate of a(t) =t+2 on t in [3, 5]?

Apr 14, 2017

6$m {s}^{- 1}$

Explanation:

we know that
$a = \frac{v}{t}$
$\therefore \frac{\mathrm{dv}}{\mathrm{dt}} = a$
so $\mathrm{dv} = a \cdot \mathrm{dt}$
$\therefore {\int}_{0}^{{v}_{t}} \mathrm{dv} = {\int}_{3}^{5} \left(t + 2\right) \mathrm{dt}$
$\implies {\left[{t}^{2} / 2 + 2 t\right]}_{3}^{5} = 12$
this yield us the net sum of velocity at the end from ${3}^{\text{rd}}$ to ${5}^{\text{th}}$ second. Now we know its been only two second sso upon dividing it with 2 may yield us the average velocity .
$\frac{12}{2} = 6 m {s}^{- 1}$