Question

please help. The position of a particle moving in a straight line during a 10–second trip is s(t) = 2t2 − 3t + 1 cm. Find a time t at which the instantaneous velocity is equal to the average velocity for the entire trip.

Answer 1

7.525

Answer 2

The average velocity is total distance traveled dived by time. In this case the total distance the particle travels is 271 cm. The time is 10 s. The average velocity is 27.1 seconds. The instantaneous velocity is given by the derivative of the position function, which in this case is\[4t-3\]. Setting that equation equal to the average velocity and solving for time gives you the answer.