In a 100m race, Usain Bolt starts from rest and speeds up with a constant accele

Question

In a 100m race, Usain Bolt starts from rest and speeds up with a constant acceleration of 5.4m/s^2 until he reaches his peak speed of 11.9m/s. He then runs with a constant speed, except for the last 12m when he starts showboating and slows down with a constant deceleration and crosses the finish line at only 8.2m/s. What is Usain's total time for the race? In a 100m race, Usain Bolt starts from rest and speeds up with a constant acceleration of 5.4m/s^2 until he reaches his peak speed of 11.9m/s. He then runs with a constant speed, except for the last 12m when he starts showboating and slows down with a constant deceleration and crosses the finish line at only 8.2m/s. What is Usain's total time for the race?

Explanation / Answer

a)

u=0

a=5.4 m/sec^2

v1=11.9 m/sec

v1=u+a*t

11.9=0+5.4*t1

===> t1=2.203 sec

distance travelled s1=ut+1/2*a*t1^2

s1=0+1/2*5.4*2.203^2

s1=13.11m

now,

b)

with constant speed v1=11.9 m/sec the total distance travelled

s2=100-(13.11+12)

s2=74.89 m

time taken t2=74.89/11.9

t2=6.29 sec

now,

c)

s3=12m

u2=v1=11.9 m/sec

v2=8.2 m/sec

now use,

v^2-u^2=2*a*s

8.2^2-11.9^2=2*a*12

===> a=-3.098m/sec^2

and

v=u+at

t3=(v2-u2)/a

t3=(8.2-11.9)/(-3.098)

t3=1.19 sec

hence

total time taken to compleate the race is,

t=t1+t2+t3

=2.203+6.29+1.194

=9.687 sec

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