A body moves on a coordinate line such that it has a position s= f(t) = t^{2}-5t+4 on the interval 0 ≤t≤8, with in meters and t in seconds.

a. Find the body’s displacement and average velocity for the given time interval.

b. Find the body’s speed and acceleration at the endpoint of the interval.

c. When , if ever, during the interval dose the body change direction?

**Solution:-**

The body’s displacement for the given time interval is 24 m.

The body’s average velocity for the given time interval is 3 m/sec.

The body’s speed at the left and right endpoint of the interval are 5 m/sec and 11 m/sec, respectively.

The body’s acceleration at the left and right endpoint of the interval are 2 m/sec^{2} and 2 m/sec^{2}, respectively.

When, if ever, during the interval does the body change direction? Selection correct choice below and fill in any answer boxes within your choice.

The body change direction at t = 5/2 sec.

please can you show the steps for this problem?