I was solving a mechanics sum

An athlete running a 100m run starts from rest and reaches the maximum speed in a distance of 15 m. He runs the remaining distance with that velocity and reaches the finish in 9.6. Calculate the initial acceleration and maximum velocity acquired by the athlete.

Kindly help me to understand the concept of this sum

  • $\begingroup$ Consider using a velocity-time graph and the areas beneath the shape created will provide the given distances. This will generate two simultaneous equations which can then be solved. From this, velocity and time can be found. $\endgroup$ – Amit Mar 23 '20 at 6:50
  • $\begingroup$ show what you have tried to do, then we may be able to help you. $\endgroup$ – kamran Mar 23 '20 at 6:56
  • $\begingroup$ This looks like a homework question. In order for such questions to be answered in this site, we need you to add details describing the precise problem you're having. What have you tried to solve this yourself? What do you mean when you ask for help with "the concept of this sum"? Please edit your question to include this information. $\endgroup$ – Wasabi Mar 23 '20 at 15:38

The runner has two types of movement: accelerating from 0 to $ v_c \quad a= \text{acceleration}$.

Let's call the constant speed Vc. So the average speed on the first 15m is half of this.

$9.6=\frac{15}{Vc/2}+\frac{85}{Vc}=\frac{2*15+85}{Vc}=115/Vc \\ 9.6Vc=115 \quad Vc=115/9.6=11.97m.s$

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    $\begingroup$ Please don't give a full answer to a homework question with no attempt at a solution. It does not serve the OP or the site well and we're not a free homework service! $\endgroup$ – Transistor Mar 23 '20 at 15:15
  • $\begingroup$ @transistor, right . Thanks. $\endgroup$ – kamran Mar 23 '20 at 16:08

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