Question

A sprinter has a final velocity of 10 m/s. If they accelerated at a constant rate of 0.5 m/s² for the final 60 m of the race, what was their velocity before they started accelerating?

a. 5 m/s
b. 7 m/s
c. 8 m/s
d. 9 m/s

Answer 1

The velocity before the sprinter started accelerating was approximately 6.325 m/s, which is closest to option d. 9 m/s.

Step-by-step explanation:

To find the velocity before the sprinter started accelerating, we can use the equation: final velocity^2 = initial velocity^2 +2 * acceleration * distance. Since the final velocity is 10 m/s, the acceleration is 0.5 m/s², and the distance is 60 m, we can substitute these values into the equation to solve for the initial velocity:

10^2 = initial velocity^2 + 2 * 0.5 * 60

Simplifying,

100 = initial velocity^2 + 60

Subtracting 60 from both sides,

40 = initial velocity^2

Taking the square root of both sides,

initial velocity = √40 ~ 6.325 m/s

The velocity before the sprinter started accelerating was approximately 6.325 m/s, which is closest to option d. 9 m/s.