Help with a 1-dimention kinematics question

[mohdhm]

Homework Statement

setting a new world record in a 100m race, maggie and judy cross the finish line in a dead heat, both taking 10.2s. Accelerating uniformly, maggie took 2.0s and judy 3.0s to attain maximum speed, which they maintained for the rest of the race. (a) what was the acceleration of each sprinter?

Homework Equations

xf=xi+vit+1/2*at^2
xf=xi+1/2(vi+vf)t
vf=vi+at

The Attempt at a Solution

tried using the 2nd equation listed to get the distance which i would then factor into the first equation ... and dealing with multi variables.. things got very messy from here... i ripped apart 3 pages from my notebook already so some help would be highly appreciated.

 

[Doc Al]

Realize that each sprinter's motion has two segments: (1) acceleration from rest to final speed, and (2) constant speed motion at the final speed. The times for these segments, as well as the total distance, are provided.

 

[Kurdt]

Yes this is a bit fiddly but you have to consider the question in two parts. The first part is when the runners are accelerating and the second is when they are traveling at constant speed.

The maximum speed reached after acceleration is thus $$v=a{t_1}^2$$

and the distance traveled is $$s=\frac{1}{2} a t_1^2$$

The distance traveled during the second part can be worked out and thus when you add the distances together you know they should make 100 and you can solve for a.

 

[apelling]

For each runner split the motion into two sections. One with uniform acceleration and one with no acceleration.

The equations you mention only apply to the motion of the runners while they accelerate. When they reach maximum velocity the only equation necessary is

x=vft

where x is the distance traveled while at max vel, vf is the max velocity achieved after accelerating and t is the time left after accelerating.

This distance plus the distance traveled while accelerating (use your first equation with xi and vi =0) adds up to 100m.
This fact should give you an equation with a and vf as unknowns. Using vf=vi+at with vi=0 you can remove vf and replace it with at, where t is the time the runner accelerated for. Now solve for a.

 

[mohdhm]

thanks for your help guys, and yes i did know that i have to solve it at 2 parts... but i couldn't solve it with either part. Thanks for your help guys. I understand it now :)