More practice questions

4. Q4. A body starts from rest with a uniform acceleration of 4 m s^⁻². How far does it go in the 3rd second?

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   Using v₀ + a(n − ½) = 0 + 4 × 2.5 = 10 m. Check: x(3) − x(2) = ½ × 4 × (9 − 4) = 10 m.

5. Q5. A ball thrown straight up returns to the thrower 4 s later. Find its launch speed and the greatest height (g = 9.8 m s^⁻²).

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   It takes 2 s to rise, so v₀ = 9.8 × 2 = 19.6 m/s. Height = 19.6^²/(2 × 9.8) = 19.6 m.

6. Q6. A stone is dropped from a tower 80 m high. One second later a second stone is thrown straight down from the same point. With what speed must it be thrown to reach the ground at the same time? Take g = 10 m s^⁻².

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   The first stone takes t with 80 = 5t^², so t = 4 s. The second has 3 s: 80 = 3v₀ + 5 × 9, so v₀ = 35/3 ≈ 11.7 m/s downwards.