Question

A particle moves according to a law of motion s = f(t) = t^3 - 9t^2 + 15t, t >= 0, where t is measured in seconds and s in feet.

a)Find the total distance traveled during the first 7 seconds

Answer 1

you have to use the arc length formula \[\int\limits_{a}^{b}\sqrt{1+(dy/dt)^2}dt\]

so you have \[\int\limits_{0}^{7}\sqrt{1+(3t^2-18t+15)^2}dt\]=71.7309