A straight slope of length 60m is inclined at an angle of 12° to the horizontal. A bobsled starts at the top of the slope with a speed of 5ms⁻¹. The bobsled slides directly down the slope.

Mark scheme

Marking points from the official mark scheme (May/June 2024). The mark or mark type is shown in brackets.

1. [B1] From mg sin12 = ma. Allow exact (e.g. a = g sin 12).
2. [M1] For use of v² = u² + 2as with u = 5 and s = 60. Allow sign errors but a must be either g sin 12 or g cos12 only.
3. [A1] AWRT 16.6
4. (M1) 3 terms, dimensionally correct. Allow sign errors; allow sin/cos mix on PE term – condone m missing from all terms. Must be a weight component.
5. (A1) Correct equation. (for reference: 60 sin12 = 12.4747...)
6. (A1) AWRT 16.6
7. [B1] Resolving correctly perpendicular to the plane.
8. [*M1] Use of Newton's second law, correct number of terms; allow sign errors; allow sin/cos mix (must be a weight component).
9. [DM1] Where R is a component of weight only (dimensionally correct but allow sin/cos mix). [a=1.79 [1.78567....]]
10. [DM1] Dependent on previous two M marks. For use of s = ut + (1/2)at² with s = 60, u = 5 and their a or other complete method to find positive value(s) of t.
11. [A1] AWRT 5.86 (from using a = 1.79 or better). AWRT 5.85 (from using a = 1.8). AWRT 5.87 (from correct working).
12. (B1) Resolving correctly perpendicular to the plane.
13. (*M1) Use of work-energy principle, correctly number of relevant terms; allow sign errors; allow sin/cos mix on PE term (must be a weight component).
14. (DM1) Where R is a component of weight only (dimensionally correct but allow sin/cos mix) [⇒v=15.5 [15.46870....]].
15. (DM1) Dependent on previous two M marks. Use of s = (1/2)(u+v)t with s = 60, u = 5 and their v or other complete method to find positive value(s) of t.
16. (A1) AWRT 5.86 [5.86260...]