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A : The acceleration-time graph for an object moving along straight line, starting from rest is as shown in figure.

Speed of the particle is maximum at time t1.

R : Velocity is maximum when acceleration is maximum.

Asked by dipanshusingla029 23rd May 2018, 5:16 PM
Answered by Expert
Answer:
 
We are given that acceleration is function of time. 
 
so we have begin mathsize 12px style fraction numerator d v over denominator d t end fraction equals space a left parenthesis t right parenthesis end style .....................(1)
where v is speed and a is acceleration
 
we can write velocity v as a functon of time from (1) as follows
 
begin mathsize 12px style v left parenthesis t right parenthesis space equals space integral subscript t superscript t plus d t end superscript a left parenthesis tau right parenthesis d tau end style
hence v(t) , i.e. velocity at time t is area under the given curve that represent the acceleration function for a small time period dt as shown in figure.
 
we can see that the area under the curve having small width dt is maximum at t = t1.
hence we can conclude speed is maximum at t = t1.
Answered by Expert 25th May 2018, 12:56 PM
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