A-LevelMathematicsMechanics9709/41 · May/June 2018 · Q47 Marks
A particle P moves in a straight line starting from a point O. At time t s after leaving O, the displacement s m from O is given by s = t³ – 4t² + 4t and the velocity is v m s¯¹.
- (i)Find an expression for v in terms of t.[2]
- (ii)Find the two values of t for which P is at instantaneous rest.[2]
- (iii)Find the minimum velocity of P.[3]
Mark scheme
Marking points from the official mark scheme (May/June 2018). The mark or mark type is shown in brackets.
- [M1] Attempt differentiation
- [A1] v = 3t² - 8t + 4
- [M1] Set v = 0 and attempt to solve a relevant 3 term quadratic
- [A1] t = ⅔ and t = 2
- [M1] Differentiate v and equate to 0
- [M1] Solve for t and attempt v
- [A1] v = -4/3
- [M1] Attempt to complete the square for v
- [M1] Find value of t for minimum v and attempt to find v
- [A1] v = -4/3
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