O-LevelAdditional MathematicsDifferentiation and integration4037/11 · Oct/Nov 2011 · Q58 Marks
A particle moves in a straight line such that its displacement, x m, from a fixed point O at time t s, is given by x = 3 + sin 2t, where t ≥ 0.
- (i)Find the velocity of the particle when t = 0.[2]
- (ii)Find the value of t when the particle is first at rest.[2]
- (iii)Find the distance travelled by the particle before it first comes to rest.[2]
- (iv)Find the acceleration of the particle when t = 3π/4.[2]
Mark scheme
Marking points from the official mark scheme (Oct/Nov 2011). The mark or mark type is shown in brackets.
- [1] (i) v = 2 cos 2t
- [1] (i) when t = 0, v = 2
- [1] (ii) cos 2t = 0, 2t = π/2
- [1] (ii) t = π/4 (0.785)
- [1] (iii) when t = π/4, x = 4
- [1] (iii) when t = 0, x = 3
- [1] (iii) distance moved = 1
- [1] (iv) a = -4 sin 2t
- [1] (iv) when t = 3π/4, a = 4
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 →