Hi I am having problems with this question below, still have no teacher to help due to corona:
A particle moves in a straight line so that, t s after leaving a fixed point O, its velocity vms-1 is given by v = 3e2t + 4t
Find the distance travelled by the particle in the third second
I can't understand why the template answer says you need to subtract the displacement at 3 seconds by the displacement at 2 seconds.
The displacement at time $t$ is given by
$$s(t) =\int_0^t v(u)du$$
since $v(t)$ is always positive, during the third second the distance travelled is
$$s(3)-s(2)=\int_2^3 v(u)du$$