The displacement (in meters) of a particle moving in a straight line is given by s=t^2-8t+17, where t is measured in seconds.

s  =  t² - 8t + 17

 

a)  Find the average velocity over these time intervals:

1)  [3, 4]    --->     t = 3   --->   s(3)  =  (3)² - 8(3) + 17  =  2

                             t = 4   --->   s(4)  =  (4)² - 8(4) + 17  =  1

     --->     average velocity  =  [ s(final) - s(initial) ] / [ t(final) - t(initial) ]

                                               =  [ s(4) - s(3) ] / [ 4 - 3 ]  =  [ 2 - 1 ] / [ 4 - 3 ]  =  1 / 1  =  1 

 

2), 3), and 4) are found in a similar fashion.

 

b)  Find the instantaneous velocity when  t = 4:

      v = s'  =  2t - 8

     --->     v(4)  =  2(4) - 8  =  0 - 0  =  0