SUVAT Displacement — Cyclist Sprint (Worked Example)

Given

• u = 8 m/s

• a = 0.6 m/s²

• t = 10 s

Find

The displacement s.

Principle

With a nonzero start speed, both SUVAT terms contribute: ut (distance at the original speed) plus ½at² (extra distance from speeding up).

Formula

Solution

1. Write the equation: $s = ut + \frac{1}{2}at^2$

2. Substitute: $s = (8)(10) + \frac{1}{2}(0.6)(10)^2$

3. First term: $80\ \mathrm{m}$; second term: $0.5 \times 0.6 \times 100 = 30\ \mathrm{m}$

4. Add: $s = 80 + 30 = 110\ \mathrm{m}$

Unit check

m/s × s = m and m/s² × s² = m — both terms are lengths.

What this means physically

110 m — the 80 m she would have covered anyway, plus 30 m gained from the sprint effort. In a race, that extra 30 m is the gap that wins.