Question

an object starts its Motion from rest and moves with constant acceleration for 5 seconds and then it retards with constant rate and comes to rest at time T = 10 seconds the ratio of average speed and maximum speed during the complete motion will be what?


pls answer it as soon as possible
I will make u brainlist

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

Therefore the velocity of the body after T=5se is :

v=u+at

v=a5

v(max)=5a

And this velocity s the maximum velocity

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

V(max)=5a

Therefore ratio of avg speed to max speed is :-

=2.5a/5a

=2.5/5

=0.5

=1/2

Hope this helps !!  ^_^