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Peter and Sanjit are running in a race. They both start from rest.

Peter accelerates uniformly, then moves at a constant speed v for 5 seconds and then decelerates uniformly, coming to rest at the finish line.

Sanjit accelerates uniformly, at the same rate as Peter, to the same speed v and then decelerates immediately, coming to rest at the finish line. He finishes the race x seconds after Peter.

Find the value of x.

I am not too sure how to tackle this problem, I have provided a sketch of a velocity time graph for this information and I thought I could compare the areas under each graph as they should be the same, however I couldn’t find a good way to do this. Here is my sketch:

enter image description here

Any ideas would be appreciated.

Jamminermit
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1 Answers1

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Say Peter takes $p$ seconds to run the entire race. Then the race is $$ \frac{p+5s}2\cdot v $$ distance long, according to the area below his graph. At the same time, it is also $$ \frac{p+x}2\cdot v $$ distance long, according to Sanjit's graph. Setting these equal, you can find $x$.

Arthur
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    Ah ok, you did have to compare the areas as I thought. I suppose I got scared away by having 3 variables in 1 equation, but it canceled down, giving x=5, thanks – Jamminermit Sep 23 '19 at 18:28