Hello, I have been practising mechanics questions and have found the question below as a revision exercise. I have answered the first part of the question but I am really struggling with the second part, which consequently leads to the third.
I would greatly appreciate if anyone could comment upon what I have calculated so far and could suggest any improvements to point me in the right direction.
Two sprinters compete in a 100m race, crossing the finishing line together after 12 seconds. The two models, A and B are models for the motions of the two sprinters:
Model A: The sprinter accelerates from rest at a constant rate for 4 seconds and then travels at a constant speed for the rest of the race.
Model B: The sprinter accelerates from rest at a constant rate until reaching a speed 9ms^-1 and then travels at this speed for the rest of the race.
1. Model A; find the maximum speed and the initial acceleration of the sprinter.
The information given is s=100m, u=0ms^-1,v=?,a=?, t=12s
v=final and maximum velocity
Use the equation v=u+at
Therefore, in the first four seconds:
v=0+a*4
v=4a
Distance travelled during the first four seconds;
s=ut+1/2at^2
s=0*4+1/2*a*4^2
s=8a
Distance travelled in the final eight seconds;
s=ut+1/2at^2
s=0*4+1/2*a*8^2
s=32a
Total distance travelled = 100m
100m=8a+32a=40a
a=100/40=2.5ms^-2
Use the value obtained for the acceleration to find the maximum velocity which was previously shown to equal; v=4a
v=2.5*4
v=10ms^-1
2. Model B; Find the time taken to reach the maximum speed and the initial acceleration of the sprinter.
This is where I am struggling, I was thinking of using the suvat equation
t=2s/u+v to find the time taken to reach 9ms^-1 but realised that without knowing the distance travelled to get there I could not do so.
Could I try to find the distance travelled using s=u^2+v^2/2a
s=0^2+9^2/2a=81/2a
Which can be rearranged that a=2s/81
Then substitute the value of a to find the time taken to reach 9ms^-1?
My apologies but I have really confused myself here.
3. Sketch distance-time graphs for each of the sprinters on the same axis. Describe how the distance between the sprinters varies in the race.
I have began to draw the graph for Model A, which I have attached, but I have excluded including Model B until I have solved part 2.
I would be grateful of any help 😁