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Mathematics · Oct / Nov 2022 · Paper 51 · Question 1

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As printed in the paper

The question as text

1. A railway truck S of mass 20 tonnes is moving along a straight horizontal track when it collides with another railway truck T of mass 30 tonnes which is at rest. Immediately before the collision the speed of S is 4 m s–1 As a result of the collision, the two railway trucks join together. Find

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Show the answer and mark scheme

  • 1(a)[2]

    v

    v

    =

    1.6(m s )

    −

    1

    v

  • 1(b)[3]

    ±

    20000(1.6

    −

    4)

    OR 30000 1.6

    ±

    ×

    48000 N s or 48 kN s

    .

    Notes for question 1

    M1 for a CLM equation, condone sign errors and extra g’s and any equivalent

    1(a)

    equation (e.g. 2 x 4 = 5v, 20 x 4 = 50v, 200 x 4 = 500v,… etc)

    OR : for equating impulses

    A1 oe Units not needed but must be positive.

    M1 impulsemomentum equation, dimensionally correct, correct no. of

    1(b)

    terms, condone sign errors but must be attempting a difference of momenta

    (allow 20 or 30 for the mass, M0 if g included or mass omitted)

    A1ft a correct equation, follow through on their v

    (allow 20 or 30 for the mass)

    N.B. If using S to find the impulse, 4 and their v must have opposite signs

    when awarding the A1ft.

    m s−) and must be positive.

    1

    A1 cao units needed (allow kg

    3

    2

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