# Find the distance traveled along a straight line with velocity equation given.

I have a fairly simple question which I just can not figure out how to solve - this is the question:

A particle travels along a straight line with its velocity at time 't' seconds given by 'v' m/s where v = 4t + 1. Find the distance traveled in the fifth second.

Any help would be appreciated, thanks.

• Integrate the expression and evaluate with with limits of 4 and 5 – David Quinn Jun 21 '15 at 10:58

As long as $t$ is present in the function we get upon Differentiating we can plug in $t=k$ to get the velocity or acceleration at time $t=k$.
$$\Rightarrow \text{Displacement over the time interval }t=4\text{ and }t=5 =\int_4^5 4t+1 dt$$ $$\bigg (2t^2+t\bigg )\bigg|^{t=5}_{t=4}$$