A particle P travels in the positive direction along a straight line with constant acceleration. P travels a distance of 52 m during the 2nd second of its motion and a distance of 64 m during the 4th second of its motion.

Mark scheme

Marking points from the official mark scheme (Oct/Nov 2022). The mark or mark type is shown in brackets.

1. [M1] 52=u(2)+0.5a(2)² - (u(1)+0.5a(1)²) or 64= u(4)+0.5a(4)² - (u(3)+0.5a(3)²) Use of s = ut + ½ at² or equivalent to form equation for 2nd or 4th second.
2. [M1] Second equation in u and a.
3. [A1] 52=u+1.5a and 64=u+3.5a Two correct equations in u and a.
4. [M1] 12=2a leading to a = 6 Solves simultaneous equations to find either u or a.
5. [A1] Initial speed = 43 ms¯¹ and acceleration = 6 ms¯²
6. [M1] s = 43×10+0.5×6×10² Use of s = ut + ½ at² or equivalent.
7. [A1 FT] Distance = 730m FT 10u+50a with u and a from part (a).