Question

Usain Bolt can sprint 100 m in 10s. He accelerates uniformly for the first 3 s of the race and then maintains a constant velocity for the final 7s of the race. Find his acceleration during the first 3s of the race. What distance does he travel in the first 3s of the race? What is the velocity when be finishes the race?

Answer 1

let the initial acceleration be a m/s^2.

initial speed=0 m/s

time of acceleration=3 seconds

final speed=initial speed+acceleration*time=0+a*3=3*a m/s

distance covered=initial speed*time+0.5*accceleration*time^2=0.5*a*9=4.5*a ma

for the next 7 seconds , he runs with uniform speed of 3*a m/s

then distance covered=speed*time=3*a*7=21*a m

total distance covered is 100 m

==>4.5*a+21*a=100

==>a=3.9216 m/s^2

part a:

his acceleration is 3.9216 m/s^2

part b:distance travelled in first 3 seconds=4.5*a=17.647 m

part c:

his final speed was 3*a=11.765 m/s