Particle, initially at rest travels in a straight line and its acceleration satisfies $$a=0.1(t-5)^2 $$for $0\leq t\leq5$
Find its average speed. during the first$5$ seconds.
I don't expect answers as this clearly is a homework, just a hint what formulas to use to find the answer. Initially I thought that it is $$\frac{\text{final velocity-initial velocity}}{2}$$
but my answer and books answer is different.
Best Answer
HINT
We need to consider an integral average for the speed $|v(t)|$ with $a(t)=\frac{dv(t)}{dt}$ for $t\in[0,5]$, that is
$$\frac{\int_0^5 |v(t)| dt}{5}$$