Mechanics question help.

A sprinter starts from rest and accelerates at 2m/s. For the first 4 seconds of the race, assume that the sprinter moved along a strsight line. Find the distance travelled in the first four seconds and the speed set the end of the first four seconds, the sprinter then travels at this speed for the remainder of this race. He travels a total distance of 100 metres, find the total time took to complete the race.. I found that the distance in first 4 secs was 16m and his speed was 8m/s but when I try find the total time taken I get 25 when the answer book says something different

Total time = T.

$T$ = 4 + time taken to run the remaining $100-16$ metres.

The time taken to run the remaining 84 metres is $\frac{84}{8}$, can you see why? He's running at a constant speed of 8 m/s over a distance of 84 metres.

So the total time is 4 + 10.5 = 14.5 seconds.

Oh yeah.. Here's me trying to use all these suvat squat ions..

Is that the right answer then?

As a general rule of thumb, you use SUVAT when you have a constant acceleration. When you don't have acceleration present in a problem, you can fall back onto the trusty distance = speed x time.

In this case, however, SUVAT would work out fine. There is a constant acceleration of a = 0 m/s^2.

So using $s = ut + \frac{1}{2}at^2$ with a = 0 would give
$84 = 8 \times t \iff t = \frac{84}{8}$.

You can see from the SUVAT equation that with a=0, it reduces to distance = speed x time anyway.

Yes you was, is it ok is I msg you with any other mechanics problems? Cheers.

Sure, it's not a problem! I'd be glad to help!

Just been going over mechanics today and one thing I completely forgot about is resultant velocities? I don't understand them (they are questions on angles etc at river banks). I am baffled do you know any sources that could help I can't find any videos on it.