O-LevelAdditional MathematicsDifferentiation and integration4037/11 · May/June 2022 · Q25 Marks
A particle moves in a straight line such that its displacement, s metres, from a fixed point, at time t seconds, t≥ 0, is given by s = (1+3t)^(1/2).
- (a)Find the exact speed of the particle when t = 1.[3]
- (b)Show that the acceleration of the particle will never be zero.[2]
Mark scheme
Marking points from the official mark scheme (May/June 2022). The mark or mark type is shown in brackets.
- [2] M1 for a(1+3t)^(-1/2)
- A1 all correct (for ds/dt = 3/2 (1+3t)^(-1/2))
- When t = 1, ds/dt = 3/16
- Speed = 3/16
- [2] B1 Allow unsimplified (for Acceleration = -27/4 (1+3t)^(-5/2))
- B1 Any valid explanation. ((1+3t)^(-5/2) is always positive (so acceleration can never be zero.))
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 →