A-LevelMathematicsMechanics9709/42 · Feb/Mar 2019 · Q69 Marks
A particle moves in a straight line. It starts from rest at a fixed point O on the line. Its acceleration at time t s after leaving O is a m s⁻², where a = 0.4t³ – 4.8t².
- (i)Show that, in the subsequent motion, the acceleration of the particle when it comes to instantaneous rest is 16 m s⁻².[6]
- (ii)Find the displacement of the particle from O at t = 5.[3]
Mark scheme
Marking points from the official mark scheme (Feb/Mar 2019). The mark or mark type is shown in brackets.
- [M1] Attempt to integrate a [∫ 0.4t³ - 4.8t² dt]
- [A1] v = 0.1t⁴ - 3.2t³ (+c)
- [DM1] Attempt to solve v = 0, and reach the form tᵃˡᵇ = k [v = 0 → 0.1t⁴ - 3.2t³ = 0]
- [M1] Attempt to solve an equation of the form tᵃˡᵇ = k [t² = 32]
- [A1] t = 4
- [B1] a = 16 m s⁻²
- [M1] Attempt to integrate v [s = [0.1t⁴ - 3.2t³ dt]]
- [A1] Correct integration. Displacement = 0.02t⁵ - 1.28t⁴
- [A1] Displacement = –9.05 m (–9.05417...)
Write your answer and get it marked
On Oracle Prep you can write or photograph your own answer and have it marked by AI against this mark scheme, with feedback on what you missed.
Sign up free →