A sprinter runs a 100 m race in a straight line. He accelerates from the starting block at a constant acceleration of 2.5 m s-2 to reach his maximum speed of 10 m s-1.

Question 8

A sprinter runs a 100 m race in a straight line. He accelerates from the starting block at a constant acceleration of 2.5 m s^-2 to reach his maximum speed of 10 m s^-1. He maintains this speed until he crosses the finish line.

Which time does it take the sprinter to run the race?

A 4 s                B 10 s              C 12 s              D 20 s

Reference: Past Exam Paper – June 2015 Paper 12 Q9

Solution:

Answer: C.

The motion consists of 2 parts:

1. motion with constant acceleration of 2.5 m s^-2

2. motion with constant speed of 10 m s^-1

Let the duration of the acceleration be t₁.

v = u + at

Time t₁ = (v – u) / a = (10 – 0) / 2.5 = 4 s

Let the distance travelled during the acceleration be s₁.

Acceleration a = 2.5 m s^-2

Initial speed u = 0 (at start)

Final speed v = 10 m s^-1

We want to find distance s₁. The equation that relates a, v, u and s is  

v² = u² + 2as

Distance s = (v² – u²) / 2a

Distance travelled s₁ = (v² - u²) / 2a = (10² – 0) / (2 × 2.5) = 20 m

The remaining distance of the 100 m race is covered at the constant speed of 10 m s^-1.

Remaining distance = 100 – 20 = 80 m

Let the time taken to cover the remaining distance be t₂.

Speed = distance / time

Time t₂ = distance / speed = 80 / 10 = 8 s

Total time taken = 8 + 4 = 12 s