The diagram shows a velocity-time graph which models the motion of a particle. The graph consists of 3 straight line segments. The velocity of the particle at time ts after passing a fixed point O is vms⁻¹. The particle leaves O with a velocity of 5 ms⁻¹ and accelerates at 0.75 ms⁻² for 20s. The particle then decelerates for the next 30s. At t = 40, the velocity of the particle is zero. After t = 40, the particle starts to travel back to O, coming to rest at O at time Ts. [Figure with v-t graph]

Mark scheme

Marking points from the official mark scheme (May/June 2025). The mark or mark type is shown in brackets.

1. [B1] Velocity at t = 20 is [5+3/4×20 =] 20 m s⁻¹ Allow if seen on diagram.
2. [B1] Speed at t = 50 is 10 ms⁻¹ When v is minimum. Allow if seen on diagram. Allow -10.
3. [*M1] Correct method to find the displacement up to t = 40 or t = 50. Follow through their 20.
4. [DM1] For an equation in T (or t) involving their displacement at either t = 40 or t = 50 and using their positive 10 which must have come from (0-their 20)/(20) x30. Must lead to a value of T>0 unless correctly recovered.
5. [A1] T = 130 Condone t = 130 or 130
6. [M1] Correct method to find the acceleration using their 10 (or -10) and their T – dependent on both M marks in part (a) and must lead to a positive value for the acceleration.
7. [A1] Acceleration = 1/8 m s⁻² or 0.125 m s⁻²