Calculus Problem Help

An object traveling on a line has velocity at time t, in meters per second, given by the function v(t)=e^t.

Solution

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Velocity is the derivative of position so position is the integral of velocity so:

s(t) = ∫v(t) dt = ∫et dt

In this case we want to know position between 0 and 1 so this becomes:

s(t) =0 ∫1 et dt

The antiderivative of et = et so s(t) = et]01 = e1 – e0 = (e – 1) meters

(assuming that time is measured in seconds)

In this case, since the function is just increasing from time 0 to time 1, the displacement is the same as the distance traveled so displacement also = (e – 1) meters or approx 1.72 meters