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The displacement (in meters) of a particle moving in a straight line is given by s = t2 − 7t + 15, where t is measured in seconds.

(a) Find the average velocity over each time interval.

(i)    [3, 4]
m/s

(ii)    [3.5, 4]
m/s

(iii)    [4, 5]
m/s

(iv)    [4, 4.5]
m/s

(b) Find the instantaneous velocity when t = 4.
m/s

Feb 7, 2019

#1
+1

[ 3, 4 ] =   (   [ (4)^2 - 7(4) + 15 ] - [ (3)^2 - 7(3) + 15 ]  ) / [ 4 - 3 ] =  0  m/s

[ 3.5, 4] = (   [ (4)^2 - 7(4) + 15 ] - [ (3.5)^2 - 7(3.5) + 15 ]  ) / [ 4 - 3.5 ]  = 0.5 m/s

[ 4, 5 ] =  (   [ (5)^2 - 7(5) + 15 ] - [ (4.5)^2 - 7(4.5) + 15 ]  ) / [ 5 - 4.5 ]   = 2.5 m/s

[ 4, 4.5 ] =  (   [ (4.5)^2 - 7(4.5) + 15 ] - [ (4)^2 - 7(4) + 15 ]  ) / [ 4.5 - 4 ]  = 1.5 m/s

To approximate the instantaneous velocity at t = 4......use this interval

[ 4, 4.001 ]  =  (   [ (4.001)^2 - 7(4.001) + 15 ] - [ (4)^2 - 7(4) + 15 ]  ) / [ 4.001 - 4 ]  ≈ 1.001 m /s

So....the instantaneous velociy at t = 4 =   1 m/s

[ If you take Calculus....you will see that this is true...!!!!]   Feb 7, 2019