What is the average speed of an object that is moving at 4 m/s at t=0 and accelerates at a rate of a(t) =2-t on t in [0,3]?

1 Answer
May 16, 2017

5.5 m/s

Explanation:

I'm assuming this is related to one-dimensional motion. Combining the integral functions for velocity and position, the equation for position with respect to time is represented by

x = x_0 + int_0^t [v_(0x) + int_0^ta_xdt]dt

So, since the initial velocity v_(0x) = 4 m/s, the postion equation with respect to time from this is

x = 4m/s(t) + 1m/(s^2)(t)^2 - 1/6m/(s^3)(t)^3

and thus the position of the object at time t = 3 is

x = 4m/s(3) + 1m/(s^2)(3)^2 - 1/6m/(s^3)(3)^3 = 16.5m

The average velocity on the interval t in [0,3] is thus

v_(av-x) = (Deltax)/(Deltat) = (16.5m)/(3s) = 5.5 m/s