1. ## Mechanical Exam Question

Given that s=ut+at^2 and that the rate of change of distance with time = speed, show that,

v=u+at

OK so it is quite simple it's a matter of differentiating the first term. But why exactly?

2. simply because velocity is defined as the rate of change of position with respect to time.

specifically ...

$v = \lim_{\Delta t \to 0} \frac{\Delta x}{\Delta t}$

3. If you were to differentiate $s(t)=ut+at^2$ you would not get $v(t)=u+at$ you would get $v(t)=u+2at$

Because $s(t)= ut+\frac {1} {2} at^2$ given that the object starts at position 0.

4. my bad, it was a typo.