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

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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}