Question

The velocity of a particle is given by v =
v0
1 + At2
, where v0 = 25 m s−1
and A = 2.0 s−2
. What
is the acceleration at t = 0? At t = 2.0 s? At t → ∞?

Answer 1

The velocity of a particle

$$v(t)=v_0(1+At^2)=25(1+2.0t^2)$$

The acceleration of a particle

$$a(t)=\frac{dv(t)}{dt}=(25(1+2.0t^2))'=100t$$

So

$$a(0)=0\:\rm m/s^2$$

$$a(2.0)=200 \:\rm m/s^2$$

$$a(\infty)=\infty$$