A sprinter who is running a 250 m race accelerates from rest at 7.5 m/s² for 1.2 s and maintains this speed for the remainder of the race. What is her time for the race?

28.37 s

Explanation:

We Have :-

Distance = 250 m

Acceleration = 7.5 m/s²

Time of Acceleration = 1.2 s

To Find :-

Total Time Taken

Formula Used :-

v = u + a * t

distance = Average speed * time

Solution :-

Let the time of constant speed be t₂

Total Time = Time of Acceleration + Time of

Constant Speed
= 1.2 + t₂
v = u + a * t

v = 0 + 7.5 * 1.2

v = 9 m/s

Average Velocity ( during acceleration ) = ( 9

+ 0 ) / 2 = 4.5 m/s

Distance = Average velocity * Time

d = 4.5 * 1.2

d = 5.4 m

Distance of Constant Speed = 250 - 5.4
= 244.6 m
Speed = 9 m/s

t₂ = distance / speed = 244.6 / 9

t₂ = 27.17 s

Total Time = 1.2 + 27.17
= 28.37 s

She completed the race in 28.37 s