Question

What must be the velocity magnitude of the automobile (from rest) after 4 seconds of travel if its acceleration is a = 2t m/s^2 along positive x-axis?

Answer 1

The velocity will be

$$v=\int^t_0at\text dt=\int^t_0(2t)t\text dt=\int_0^42t^2\text dt=\frac23t^3\bigg|^4_0=\\\space\\ =\frac23(4^3-0^3)=42.67\text{ m/s}.$$