Calculus problem help

Question

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

Answer 1

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

s(t) = ∫v(t) dt = ∫e^t dt

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

s(t) =₀ ∫¹ e^t dt

The antiderivative of e^t = e^t so s(t) = e^t]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