A body moves on a coordinate line such that it has a position s = f(t) = t^2 - 3

Question

A body moves on a coordinate line such that it has a position s = f(t) = t^2 - 3t + 2 on the interval 0 lessthanorequalto t lessthanorequalto 9, with s in meters and t in seconds Find the body's displacement and average velocity for the given time interval Find the body's speed and acceleration at the endpoints of the interval C. When, if ever, during the interval does the body change direction? The body's displacement for the given time interval is 54 m (Type an integer or a simplified fraction) The body's average velocity for the given time interval is 6 m/sec (Type an integer or a simplified fraction.) The body's speeds at the left and right endpoints of the interval are m/sec and m/sec, respectively. (Type integers or simplified fractions.)

Explanation / Answer

body's displacement s=92-3*9+2=56

average velocity =displacement/time =56/9

as speed =ds/dt =2t-3

hence at left end speed =2*0-3 =-3

and at right end speed =2*9-3 =15

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