Two cyclists, Isabella and Maria, are having a race. They both travel along a straight road with constant acceleration, starting from rest at point A. Isabella accelerates for 5 s at a constant rate a ms⁻². She then travels at the constant speed she has reached for 10 s, before decelerating to rest at a constant rate over a period of 5 s. Maria accelerates at a constant rate, reaching a speed of 5 ms⁻¹ in a distance of 27.5 m. She then maintains this speed for a period of 10s, before decelerating to rest at a constant rate over a period of 5 s.

Mark scheme

Marking points from the official mark scheme (May/June 2021). The mark or mark type is shown in brackets.

1. [B1] Isabella v=5×1.1 [=5.5] Isabella's constant speed for 10 seconds
2. [M1] Use of s = ut + ½at² or use of v–t graph to find total distance For either Isabella or Maria, all sections included but allow one error in use of formulae
3. [A1] S_I = ½ × 1.1 × 5² + 10 × 5.5 + ½ × 1.1 × 5² [= 82.5] or S_I = ½ × (20+10) × 5.5 [= 82.5] For correct expression for Isabella, accept unsimplified
4. [A1] S_M = 27.5 + 5 × 10 + ½ × 5 × 5 [= 90] For correct expression for Maria, accept unsimplified
5. [B1] Distances for Isabella = 82.5 and Maria = 90, so Maria goes further
6. [M1] ½ a × 5² + 10 × 5a + ½ a × 5² = 90 or ½ × (20+10) × 5a = 90 Attempt total distance travelled by Isabella and set up an equation for a, using their value of S_M = 90. All parts included, allow one error.
7. [A1] a = 1.2