What is her final speed after this elapsed time? how much time did she save compared to continuing at her initial speed?

Question

A cyclist sprints at the end of her road race in an attempt to clinch a victory. She has an initial speed of 9.5m/s9.5m/s and accelerates at a rate of 0.50m/s^2 for 7.00s. Include units as appropriate below.

(a) What is her final speed after this elapsed time?

(b) She then continues at this speed to the finish line. If she was 300m300m from the finish line when she started to accelerate, how much time did she save compared to continuing at her initial speed?

Answer 1

A cyclist sprints at the end of her road race in an attempt to clinch a victory. She has an initial speed of 9.5m/s and accelerates at a rate of 0.50m/s^2 for 7.00s.

Mathematically it looks like this:

Start of Sprint: 9.5 m/s

Sprint +1s: 10m/s

Sprint +2s: 10.5m/s

Sprint +3s: 11 m/s

Sprint +4s: 11.5 m/s

Sprint +5s: 12 m/s

Sprint +6s: 12.5m/s

Sprint +7s: 13m/s

A) Final Speed = 0.5m/s (7 seconds) + 9.5 m/s = 13m/s

B) She then continues at this speed to the finish line. If she was 300m from the finish line when she started to accelerate, how much time did she save compared to continuing at her initial speed?

Without acceleration = 300m ÷ 9.5m/s = 31.57s

With acceleration:

Start of Sprint: 9.5 m/s

Sprint +1s: +10m/s

Sprint +2s: +10.5m/s

Sprint +3s: +11 m/s

Sprint +4s: +11.5 m/s

Sprint +5s: +12 m/s

Sprint +6s: +12.5m/s

Sprint +7s: +13m/s

7 seconds of acceleration = 90m:

210m left at 13m/s (210m ÷ 13m/s) = 16.15s + 7 original accelerations seconds = 23.15s

Without acceleration - with acceleration = seconds faster

31.57s - 23.15s = 8.42s saved by accelerating