# Find the maximum speed of the elevato

## Homework Statement

A person of mass mp stands on a scale in an elevator of mass me . The scale reads the magnitude of the force F exerted on it from above in a downward direction. Starting at rest at t=0 the elevator moves upward, coming to rest again at time t=t_0. The downward acceleration of gravity is g . The acceleration of the elevator during this period is shown graphically above and is given analytically by ay(t)=α−2αt_0t

a) Find the maximum speed of the elevator. Express your answer in terms of α and t0

b) Find the total distance traveled by the elevator. Express your answer in terms of α and t0 (enter alpha for α and t_0 for t0)

## The Attempt at a Solution

I got part a right (answer is 1/4*alpha*t_0) but I don't know how to get b I tried integrating the velocity with repsect to t with the limits of t_0 and 0 and I got 1/4*a*t_0^2, but that is not right. Can someone please tell me what I;m doing wrong?

## Answers and Replies

What is the velocity function and how do you integrate it?