Question

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

Answer 1

The required ratio of avg velocity to max velocity is 1:2

Answer 2

Answer: 1 : 2

Explanation:

In the first part of the motion where the object is accelerating,

initial velocity, u = 0

time taken, t = 5 s

let constant acceleration be a

from equation of motion, the final velocity is

v=u+at⇒v=0+a×5⇒v=5a

for the second half of the motion where object is decelerating,

initial velocity, u'=v= 5a

final velocity, v'=0

time taken, t'=10 s-5 s=5 s

acceleration, a = -a

the maximum speed = 5a

the average speed = total distance / total time

total time = 10 s

Total distance, d=ut+0.5at²+u't'+0.5a't'²

⇒d=0+0.5×a×5²+5a×5+0.5×(-a)×5²=25a

Average speed = 25 a÷10=2.5 a

The ratio of average speed to maximum speed is:

2.5 a : 5 a =1 : 2

Hence, the ratio of average speed and maximum speed during the complete motion will be 1:2