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(\frac{\tau^2}2+6\tau\right)\bigg|_(\tau=0)^(\tau=t)`

`v(t)=4+\frac{t^2}2+6t`