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
+128474 [ 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...!!!!]
