A-LevelMathematicsMechanics9709/42 · Feb/Mar 2020 · Q710 Marks
A particle moves in a straight line through the point O. The displacement of the particle from O at time t s is s m, where s = t² - 3t + 2 for 0 ≤ t ≤ 6, s = 24/t - t²/4 + 25 for t ≥ 6.
- (a)Find the value of t when the particle is instantaneously at rest during the first 6 seconds of its motion.[2]
- (b)Find the velocity with which the particle arrives at P and also the velocity with which the particle leaves P.[3]
- (c)Find the total distance travelled by the particle in the first 10 seconds of its motion.[5]
Mark scheme
Marking points from the official mark scheme (Feb/Mar 2020). The mark or mark type is shown in brackets.
- [M1] For differentiation of s for 0 ≤ t ≤ 6
- [A1]
- [B1] t = 6 used in v
- [M1] For differentiation of s for t ≥ 6
- [A1] Allow v = –11/3
- [B1] SOI
- [B1] SOI
- [B1] SOI
- [M1] Evidence of distance rather than displacement involving all three sections, (0, 1.5), (1.5, 6) and (6, 10)
- [A1]
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