Answer :
The sprinter will finish the 100m race in 9.90 seconds if he runs at constant speed of 10.1 m/s.
In order to find the time that the sprinter will take to finish the 100 m race if he maintains constant speed of 10.1 m/s for the last part of the race.
The acceleration can be found using the relation,
a = (v₂ - v₁)/t, v₂ and v₁ are the final and initial speed of the sprinter and a ant t are time acceleration and time of the sprinter in the race.
= (10.1m/s-0m/s)/2.2 s
= 4.59 m/s²
Now, using the kinematic equations of motion to find the time that the sprinter will take,
x = v₁t + (1/2)at²
100 m = 0 + (1/2)4.59m/s²(t²)
t = √(100m x 2/4.59m/s²)
= 4.95 seconds.
Now, adding the time that sprinter take to cover the last part to get the final time to finish the race.
T = 4.95s+(100m/10.1m/s)
= 9.90 seconds.
Therefore, the sprinter will finish the 100m race in 9.90 seconds with a constant speed of 10.1m/s that he maintains at the end.
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