O-LevelAdditional MathematicsDifferentiation and integration4037/12 · May/June 2017 · Q56 Marks
A particle P moves in a straight line, such that its displacement, x m, from a fixed point O, t s after passing O, is given by x = 4 cos (3t) – 4.
- (i)Find the velocity of P at time t.[1]
- (ii)Hence write down the maximum speed of P.[1]
- (iii)Find the smallest value of t for which the acceleration of P is zero.[3]
- (iv)For the value of t found in part (iii), find the distance of P from O.[1]
Mark scheme
Marking points from the official mark scheme (May/June 2017). The mark or mark type is shown in brackets.
- [B1] v = -12 sin 3t
- [B1] 12
- [B1] a = -36 cos 3t
- [B1] 3t = π/2 ≈ 1.57 or better
- [B1] t = π/6 or 0.524
- [B1] 4 cao
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 →