A particle, P, travels in a straight line, starting from a point O with velocity 6 ms⁻¹. The acceleration of P at time t s after leaving O is a ms⁻², where a = -1.5t^(1/2) for 0 ≤ t ≤ 1, a = 1.5t^(1/2) - 3t^(-1/2) for t > 1.

Mark scheme

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

1. [M1] Increase power by 1 and a change in coefficient in at least one term (which must be the same term); v=at is M0. Expect (v=)-t^(3/2) [+c].
2. [A1] Allow for -t^(3/2) + c and c=6 seen from CWO. Allow unsimplified.
3. [A1] CWO.
4. [*M1] Increase power by 1 and a change in coefficient in at least one term (which must be the same term); v=at is M0.
5. [DM1] Must get a numerical expression for c; if no substitution seen, c must be correct for their expression for v. Their 5 must not be a made up value.
6. [A1] OE, but must be a complete (possibly unsimplified) expression.
7. [*M1] For attempt at integration of their v for either section
8. [A1] For either correct. Allow unsimplified.
9. [DM1] Using correct limits correctly, in expressions that have come from integration (where all powers must have increased by 1 with a change in coefficient for non-linear terms) of a v that came from integration, and using the limits correctly would lead to 2 positive values when used in their expressions. s₁ and s₂ must have the correct number of non-constant terms and must include a linear term.
10. [A1] Total distance = 20m