A train of mass 180000kg ascends a straight hill of length 1.5km, inclined at an angle of 1.5° to the horizontal. As it ascends the hill, the total work done to overcome the resistance to motion is 12000 kJ and the speed of the train decreases from 45ms⁻¹ to 40ms⁻¹.

Mark scheme

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

1. [B1] 180000g×1500sin1.5...
2. [B1] For initial KE or final KE (for reference: difference in KE is 38 250 000).
3. [M1] Correct number of terms; dimensionally correct; allow sign errors and minor slip(s) in values; allow sin/cos mix on PE term. Work done = (70677760.4...+12000000–38250000) J = (70677.7...+12000–38250)kJ
4. [A1] Must be in kJ.
5. (B1) Correct acceleration from 40² = 45² + 2a(1500). Allow AWRT -0.14 or exact -17/120.
6. (M1) M1 for applying Newton's second law parallel to the hill. Correct number of terms, allow sin/cos mix on weight component, dimensionally correct and multiplying both sides by 1500. Allow their a or a for acceleration (and minor slip(s) in values).
7. (B1) Correct weight component multiplied by 1500.
8. (A1) Must be in kJ.