Question

Suppose that in t hours, a truck travels s(t) miles, where s(t)= 10t² . Find the average rate of change of distance with respect to time from t1 = 2 and t2 = 5.

Answer 1

The rate of change of distance

$v(t)=\frac{d}{dt}s(t)=\frac{d}{dt}(10t^2)=20t$

The average rate of change of distance with respect to time from $t_1=2$ and $t_2 = 5$.

$<v(t)>=\frac{1}{t_2-t_1}\int_{t_1}^{t_2}v(t)dt=\frac{1}{5-2}\int_{2}^{5}20tdt=$$\frac1310t^2|_2^5=\frac1310(25-4)=70$ (miles/hour).