The displacement (in meters) of a particle moving in a straight line is given by

Question

The displacement (in meters) of a particle moving in a straight line is given by s=t^2-8t+15 where t is measured in seconds. (A) (i) Find the average velocity over the time interval [3,4]. Average Velocity = (ii) Find the average velocity over the time interval [3.5,4]. Average Velocity = (iii) Find the average velocity over the time interval [4,5]. Average Velocity = (iv) Find the average velocity over the time interval [4,4.5]. Average Velocity = (B) Find the instantaneous velocity when . Instantaneous velocity =

Explanation / Answer

FOLLOW THIS The displacement s=t^2-8t+18, where 't' is in seconds and 's' is in meters The displacement at t=4 s(4 )=4^2 -8*4 +18 s(4 )=16 - 32 +18 =2 m The displacement at t=3 s(3 )=3^2 -8*3 +18 s(3 )=9 - 24 +18 = 3 m s(4) - s(3) =2 -3 = -1 m Average velocity = v = displacement / time (a)Average velocity = v = -1 / 1 = - 1 m/s ______________ The displacement at t=5 s(5 )=5^2 -8*5 +18 s(5 )=25 - 40 +18 =3 m The displacement at t=4 s(4 )=4^2 -8*4 +18 s(4 )=16 - 32 +18 =2 m s(5) - s(4) =3 - 2 = 1 m Average velocity = v = displacement / time (b)Average velocity = v = 1 / 1 = 1 m/s _______________________________ Instantaneous velocity v = ds/dt = 2t - 8 Instantaneous velocity when t=4, v =2*4 -8 v =8 -8 = 0 2.Instantaneous velocity when t=4 is zero

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