A body starts moving from rest on a smooth horizontal surface. The acceleration, a, of the body is given by the equation ( t - 1) m/s2 , where t is the time elapsed in seconds from the start. Determine its average velocity at t = 5 s.

a) v = 7.50 m / s            
b) v = 3.75 m / s 
c) v = 1.67 m / s .

d) v = 8.33 m / s .

 

Since the acceleration is a function of time, the velocity is given by,
         
   dv = (t - 1 ) dt

integrating both sides,
   
At t = 5 seconds the Velocity is given by,
     v = ( 52 / 2 - 5 ) = 7.5 m/s

The displacement from the initial position is given by,          
     

At t = 2 s the displacement is

   s = ( 23 / 6  -  22 / 2) = - 0. 66 m .

At t = 5 s the displacement is given by,.

   s = ( 53 / 6  -  52 / 2) = 8.33 m

The average velocity is given by
 vav = Total displacement / Total time taken.
 vav = 8.33 / 5 = 1.67 m/s.

Hence the average velocity is 1.67 m/s.