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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.

Hancho
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1 Answers1

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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

$$s(3)-s(2)=\int_2^3 v(u)du$$

user
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