Question

The position of particle x varies with time according to relation x = ( t² + t - 3 ) m. Its average velocity during t = 2s to 5 s is

Answer 1

x= t^2+t-3 
At t = 5 , x = 25+5-3 = 27
At t=2, x=4+2-3=3
Change in displacement = 27-3=24

Change in time  = 5-2 = 3 sec
Avg velocity  = Change in disp / Change in time = 24/3 = 8m/s

Answer 2

x = t^2 + t + 3
Displacement at t = 2
x = 2^2 + 2 + 3
x = 9 m

Displacement at t = 5
x = 5^2 + 5 + 3
x = 33 m

Average velocity = Displacement / Time
= (33 - 9) / (5 - 2)
= 8 m/s