Sprinting Question Involving Constant Acceleration

[Emethyst]

Homework Statement

The world record for the 100m dash is 9.58s, and for the 60m dash it is 6.38s. Assume a sprinter accelerates at a constant rate up to a maximum velocity that is maintained for the rest of the race, no matter how long it is.

a) Find the acceleration (both sprinters will have the same acceleration)
b) Find the duration of this acceleration
c) Find the maximum velocity achieved by this acceleration
d) The world record for the 200m dash is 19.19s, while for the 1000m run it is 131.96s. Are these times consistent with the assumptions made?

Homework Equations

Kinematic equations

The Attempt at a Solution

This question is really stumping me. I know that I have to link the two values given to find the acceleration in part a, and thus everything else asked for, but I'm not sure how to go about doing this. My guess was to first find the each of the accelerations for the values given and then average them, but this does not seem to be the right way to solve for it. If anyone can point me in the right direction here it would be greatly appreciated, thanks in advance.

 

[method_man]

Homework Statement

The world record for the 100m dash is 9.58s, and for the 60m dash it is 6.38s. Assume a sprinter accelerates at a constant rate up to a maximum velocity that is maintained for the rest of the race, no matter how long it is.

a) Find the acceleration (both sprinters will have the same acceleration)
b) Find the duration of this acceleration
c) Find the maximum velocity achieved by this acceleration
d) The world record for the 200m dash is 19.19s, while for the 1000m run it is 131.96s. Are these times consistent with the assumptions made?

Homework Equations

Kinematic equations

The Attempt at a Solution

This question is really stumping me. I know that I have to link the two values given to find the acceleration in part a, and thus everything else asked for, but I'm not sure how to go about doing this. My guess was to first find the each of the accelerations for the values given and then average them, but this does not seem to be the right way to solve for it. If anyone can point me in the right direction here it would be greatly appreciated, thanks in advance.

Hy. I would like to point you on this key sentence

Assume a sprinter accelerates at a constant rate up to a maximum velocity that is maintained for the rest of the race

O.K. So, each displacement consists of 2 time intervals. First interval is when they accelerate, and the second one is when they run with constant speed.
Your displacement formula would be s=1/2*a*t²+v_max*t₁
This formula you must use for 100 m and for 60 m race. You know that v_max=a*t. Time t is equal for both races, and time t₁ will be different. Total time which is given for both races is equal to t+t₁.