Question

A jeepney's velocity over time in ft/sec as it moves along the x-axis is governed by the function v(t)=3t^2-10t+15. If the jeep's position at t= 1 second is 8ft, what is the total displacement made by the jeepney from t=0 to t=5sec?

please I need help, i just need the idea on how to solve this

Answer 1

s = integral v dt

s = t^3 - 5 t^2 + 15 t + c
when t = 1, s = 8
8 = 1 - 5 + 15 + c
c = -3
so
s = t^3 - 5 t^2 + 15 t - 3

then when t = 0, s = -3
when t = 5
s = 125-125 + 75 -3 = 72
so the jeepney (whatever that is) went from -3 to + 72 or 75 ft