# Difficult kinematics/power question

1. A sprinter, whose mass is 75 kg, runs a 50 meter dash. The total elapsed time is 8.5 seconds. The sprinter accelerates at a constant rate over the first second and runs the rest of the race at constant velocity.

a. Calculate the average power produced for the first second.
b. What is the maximum power the sprinter generates?

hint: Displacement over the 1st second plus displacement over the rest of the race = 50 meters.

2. Kinematics: D=(v0+v1)/2)*t, P=w/t, P=Fv

3. i tried putting 50=(0+v1)/2)*8.5 to get V, but since there are two diffrent speeds because he accelerates, I don't think this is right. I put 0 for V0, d=5-, and t=1 and tried to solve for A, but to no avail.

Any help would be appricated.

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#### Shooting Star

Homework Helper
Avg power = total energy expended/time.

If v is the speed at the end of one sec, then (1/2)mv^2 is the total energy spent in 1 s.

Find v from kinematics. Try to figure out the rest.

Ok, for kinematics to solve for V, is 50=((0+V)/2)*8.5 right? Does this give me his constant velocity over the 50m?

I got 11.76 M/S when solving that, that seems a bit too fast...it this correct?

#### Shooting Star

Homework Helper
Ok, for kinematics to solve for V, is 50=((0+V)/2)*8.5 right? Does this give me his constant velocity over the 50m?
No. He has not gone at a const v for 50 m, neither he has accelerated for 50 m.

He has accelerated only for the first one second, for a dist of d say, and travelled at the same speed v for the rest 7.5 s over a dist of 50-d. Find the relations between v and d considering accn over the dist d, and again considering const speed over the dist 50-d. Your aim is to find v.

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