Asprinter practicing for the 200-m dash accelerates uniformly from rest at a and reaches a top speed of 34 km/h at the 78-m mark. he then maintains this speed for the next 59 meters before uniformly slowing to a final speed of 30 km/h at the finish line. determine the maximum horizontal acceleration which the sprinter experiences during the run. where does this maximum acceleration value occur?

The maximum acceleration experienced by the sprinter is and it is experienced in the first phase when the sprinter starts his sprint.

Explanation:

Since the sprinter attains a final speed of 34 km/h  in  runing 200 meters while starting from rest we have

Using the third equation of kinematics we have

where

v is the final speed

u is the initial speed

a is the acceleration

s is the distance covered

Since it is given that sprinter starts from rest thus u= 0 m/s and v= 34 km/h = 9.4m/s this speed is attained at s = 78 m

Applying values in the above equation we get

Since after that the sprinter moves at a constant velocity thus in that phase it's acceleration is

Now since the sprinter decelerates to 30 km/h or 8.33 m/s in final 63 meters thus  the deceleration experienced is again found by third equation of kinematics as

Upon comparing the maximum acceleration experienced by the sprinter is