Question

an object starts its Motion from rest and moves with constant acceleration for 5 seconds and then it retards with constant rate and come to rest at time t=10s. the ratio of average speed during the complete motion will be

Answer 1

Hey Champ !


Well these questions are based on Kinematic equation

And we know average speed = Total distance/Total time


For first case when the particle is accelerating with a constant acceleration of "a" (say)

therefore

the distance travelled by it is

s=ut+1/2at^2

s=1/2*a*(5)^2

s=1/2*a*25

and the time taken cover this distance is T1= 5sec

For the second case when object starts retarding let the retardation magnitude be "r"

V=u+at

0=5a-r(10)

r=5a/10

r=a/2

Hence the distance travelled during the retardation is

s=ut+1/2at^2

s=(5a)10-1/2*a/2*(10)^2

s=50a-100/4*a

s=50a-25a

s=25a


and the time required for this is 10 seconds


Therefore average velocity = Total distance /Total time


Avg Velocity = (25/2*a+25a)/(5+10)

                     =75a/(15*2)

                       =75a/30

                      =2.5a


Hope this helps!! ^_^