A-LevelMathematicsMechanics9709/43 · May/June 2021 · Q610 Marks
A particle moves in a straight line and passes through the point A at time t = 0. The velocity of the particle at time t s after leaving A is v m s⁻¹, where v = 2t² – 5t + 3.
- (a)Find the times at which the particle is instantaneously at rest. Hence or otherwise find the minimum velocity of the particle.[4]
- (b)Sketch the velocity-time graph for the first 3 seconds of motion.[3]
- (c)Find the distance travelled between the two times when the particle is instantaneously at rest.[3]
Mark scheme
Marking points from the official mark scheme (May/June 2021). The mark or mark type is shown in brackets.
- [M1] Attempt to solve v = 0
- [A1]
- [M1] Uses roots or dv/dt=0 to find t for vmin and attempts substitution to obtain vmin. Alternatively completes square.
- [A1]
- [B1]
- [B1] 3 of the 5 key points shown on axes or as coordinates
- [B1]
- [M1] For use of s = ∫v dt
- [M1] Correct use of limits (their 1 and 1.5)
- [A1] A0 for -0.0417
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