Answer to Question #161402 in Calculus for Johnny Tim

Question

The position of a particle is given by the function s (t) = (2t - 3)e^2-t for t > 0. What is the average velocity of the particle from t = 1 to t = 3?

Leave your answer in terms of e, not a decimal.

Answer 1

Solution:

The position of a particle is given by the function s(t) = (2t - 3)e^2-t for t > 0.

we have to find the average velocity of the particle from t=1 to t=3

{ Average velocity = $\frac{ s(t2) - s(t1)}{t2 - t1}$ , where s(t1) and s(t2) are position of particle at time t1 and t2 respectively}

here given t1 = 1 and t2 = 3

s(t1) = s(1) = (2*1 - 3)e^2-1 = -e

s(t2) = s(3) = (2*3 - 3)e^2-3 = 3e^-1

therefore,

Average velocity = $\frac{ s(t2) - s(t1)}{t2 - t1}$ = $\frac{ s(3) - s(1)}{3-1}$ = $\frac{ 3}{2}$ e^-1 + $\frac{ 1}{2}$ e