More practice questions

4. Q4. A particle at r₀ = (2î + 1ĵ) m has v₀ = (3î) m/s and a = (−1î + 2ĵ) m s^⁻². Find its position at t = 2 s.

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   r = r₀ + v₀t + ½at^² = (2 + 6 − 2)î + (1 + 0 + 4)ĵ = (6î + 5ĵ) m.

5. Q5. In Q4, when is the x-component of velocity zero, and where is the particle then?

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   v_x = 3 − t = 0 at t = 3 s. Then x = 2 + 9 − 4.5 = 6.5 m and y = 1 + 9 = 10 m: at (6.5 m, 10 m), with instantaneous velocity along +y at v_y = 6 m/s; the curved trajectory does not become a straight line.

6. Q6. A ball rolls off a horizontal table at 2 m/s. Taking g = 10 m s^⁻², find its position relative to the table edge after 0.3 s, assuming it remains airborne and air resistance is negligible.

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   Horizontally: x = 2 × 0.3 = 0.6 m. Vertically, from rest: y = −½ × 10 × 0.09 = −0.45 m. So it is 0.6 m out and 0.45 m below the edge.