A-level Physics (Advancing Physics)/Kinematics/Worked Solutions

1. A person accelerates from a speed of 1 ms⁻¹ to 1.7 ms⁻¹ in 25 seconds. How far has he travelled in this time?

u = 1, v = 1.7, t = 25

$s={\frac {u+v}{2}}t={\frac {1+1.7}{2}}\times 25=1.35\times 25=33.75{\mbox{m}}$

2. A car accelerates at a rate of 18 kmh⁻² to a speed of 60 kmh⁻¹, travelling 1 km in the process. How fast was the car travelling before it travelled this distance?

a = 18, v = 60, s = 1

v² = u² + 2as

60² = u² + (2 x 18 x 1)

3600 = u² + 36

u² = 3564

u = 59.7kmh⁻¹ (to 3 significant figures)

3. A goose in flight is travelling at 4 ms⁻¹. It accelerates at a rate of 1.5 ms⁻² for 7 seconds. What is its new speed?

u = 4, a = 1.5, t = 7

v = u + at = 4 + (1.5 x 7) = 14.5 ms⁻¹

4. How far does an aeroplane travel if it accelerates from 400 kmh⁻¹ at a rate of 40 kmh⁻² for 1 hour?

u = 400, a = 40, t = 1

$s=ut+{\frac {at^{2}}{2}}=(400\times 1)+{\frac {40\times 1^{2}}{2}}=420{\mbox{km}}$