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A particle starts from rest and traverses a distance l with uniform acceleration, then moves uniformly over a further distance 2l and finally comes to rest after moving a further distance 3l under uniform retardation. Assuming entire motion to be rectilinear motion, the ration of average speed over the journey to the maximum speed on its way is:

Asked by Arushi Juyal 12th November 2017, 3:22 PM
Answered by Expert
Answer:
The entire travel is divided into three parts (1) accelerated travel (2) Uniform speed travel (3) travel with retarding speed
 
for each part let us assume the time duration is t1 , t2 and t3.
 
For the part-1, let us assume the acceleration is a.
The duration t1 and the final velocity at the end of part-1 travel distance l  is given by
From the above equations we can get
 
 
 
For the second travel part, which is travelled with uniform speed   a×t1 , we get the relation for
distance travelled as given below and we can get the relation for travel duration t2 
 
for third part, initial velocity is at1  and this motion is retarded and let us assume retardation is r. 
By considering the travel distance 3l and final velocity is zero we get the following two equations 
 
By substituting for t1 in the above second equation we get   r = a/3.
 
Substituting for r and t1 in the first equation, we get 
 
So the required ratio of average speed to maximum speed is given by 
By Substituting for t1, t2 and t3, we will get the ratio as 3/5 after simplification


Answered by Expert 13th November 2017, 12:01 PM
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