MATA32 – Winter 2010
Quiz 7 Solutions
1. Suppose the position function of an object moving along a number line is given by
s=f(t) = 2t3
−7t+ 1, where tis in seconds and sis in meters.
(a) Find the average velocity over the interval [2,2.1].
The total distance traveled between the time t= 2 and t= 2.1is
f(2.1) −f(2) = 1.822 m
Since it took 0.1 s for the object to move this distance, the average
velocity is 18.22 m/s.
(b) Find the velocity when t= 2.
The velocity at time tis the derivative of the position, i.e. it’s
f0(t) = 6t2
Therefore, the velocity at t= 2 is f0(2) = 17 m/s.
Continued on reverse...