A-LevelMathematicsMechanics9709/42 · Oct/Nov 2017 · Q36 Marks

A car travels along a straight road with constant acceleration. It passes through points A, B and C. The car passes point A with velocity 14 m s⁻¹. The two sections AB and BC are of equal length. The times taken to travel along AB and BC are 5 s and 3 s respectively.

(i)Write down an expression for the distance AB in terms of the acceleration of the car. Write down a similar expression for the distance AC. Hence show that the acceleration of the car is 4 m s⁻².[4]
(ii)Find the speed of the car as it passes point C.[2]

Mark scheme

Marking points from the official mark scheme (Oct/Nov 2017). The mark or mark type is shown in brackets.

[B1] SAB = 14 x 5 + ½a × 5² or SAB = ½(14+ 14 + 5a) × 5 OE
[B1] SAC = 14 x 8 + ½a × 8² or SAC = ½(14+ 14 + 8a) × 8 OE
[M1] [112 + 32a = 2(70 + 12.5a)] Using AC = 2AB and solving for a or for substituting a = 4 and finding AB and AC
[A1] a = 4 m s⁻² AG, If substituting a = 4 must show AB = 120 and AC = 240 OE
[M1] [v = 14 + 4 × 8] Use of v = u + at or any complete method to find v
[A1] Velocity = 46 m s⁻¹

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.

Topic: Mechanics, A-Level Mathematics (syllabus 9709). Structured question, 6 marks.
Source: A-Level Mathematics, Oct/Nov 2017 Paper 4 Variant 2, question 3.

Questions and mark schemes are from past examination papers and remain the copyright of the exam board. How Oracle Prep builds its content