Question

The acceleration function (in m/s2) and the initial velocity are given for a particle moving along a line. a(t) = t + 6, v(0) = 4, 0 ≤ t ≤ 11 (a) find the velocity at time t.

Answer 1

Given the acceleration $a(t)=t+6$, the velocity is

$v(t)=v(0)+\displaystyle\int_{\tau=0}^{\tau=t}a(\tau)\,\mathrm d\tau$

$v(t)=4+\left(\dfrac{\tau^2}2+6\tau\right)\bigg|_{\tau=0}^{\tau=t}$

$v(t)=4+\dfrac{t^2}2+6t$