A-LevelMathematicsMechanics9709/51 · May/June 2017 · Q79 Marks
A particle P of mass 0.5 kg is at rest at a point O on a rough horizontal surface. At time t = 0, where t is in seconds, a horizontal force acting in a fixed direction is applied to P. At time t s the magnitude of the force is 0.6t² N and the velocity of P away from O is v m s⁻¹. It is given that P remains at rest at O until t = 0.5.
- (i)Calculate the coefficient of friction between P and the surface, and show that dv/dt = 1.2t² - 0.3 for t > 0.5.[3]
- (ii)Express v in terms of t for t > 0.5.[3]
- (iii)Find the displacement of P from O when t = 1.2.[3]
Mark scheme
Marking points from the official mark scheme (May/June 2017). The mark or mark type is shown in brackets.
- [B1] μ = 0.6 × 0.5² / (0.5 g) ( = 0.03)
- [M1] 0.5dv / dt = 0.6 t² – 0.03 × 0.5g
- [A1] dv/dt = 1.2 t² - 0.3
- [M1] ∫dv = ∫(1.2t² – 0.3) dt
- [M1] t = 0.5, v = 0 hence c = 0.1
- [A1] v = 0.4t³ -0.3t + 0.1
- [M1] ∫dx = ∫(0.4t³ – 0.3t + 0.1) dt
- [M1] t = 0.5, x = 0 hence c = -0.01875
- [A1] x(1.2) = 0.0926(1)
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 →