Find Maximum Speed of Athlete in 100m Sprint - Solve with Integration

[Junkwisch]

In a 100 metre sprint, an athlete reaches her maximum speed in 3.0 seconds, starting from rest, assuming constant acceleration. She maintains her maximum speed until the finish, with an overall time of 11.0 seconds. Determine her maximum speed, vmax.


I'm trying to solve this problem but it is with little successes, I realized that this is not a constant motion (she stop accelerating). Thus I have to solve it with some kind of integration. Can anyone tell me what equation do I have to use?

 

[adjacent]

No, you don't need calculus here. Her acceleration was constant and she reached the maximum speed in 3 seconds and covered a distance of 100m.
You can use the kinematics equation involving final velocity, initial velocity, distance and time

 

[Junkwisch]

But I don't know what her acceleration is, even though it is constant for the first three seconds. Since I do not know her displacement in the last eight seconds.

 

[adjacent]

But I don't know what her acceleration is, even though it is constant for the first three seconds. Since I do not know her displacement in the last eight seconds.

Oh, I think I misinterpreted the question. What you can do is draw a sketch of the velocity time graph. You don't know the velocity so leave the y-axis empty. Since the area under the graph is the distance , you can find the velocity.
It should be in a trapezium shape.

 

[Junkwisch]

Thankyou so much adjacent, it worked :D

 

[adjacent]

You are welcome