May/June 2026 Paper 42

2026 · 7 questions · 14 parts · 50 marks

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Context for question 7

A particle

P

moves in a straight line. The velocity

v m/s

of

P

at time

t s

, where

t \geq 0

, is given by

v = k_{1} (4 t + 11)^{\frac{1}{2}} - \frac{1}{4} (2 t + 1)^{2} + k_{2},

where

k_{1}

and

k_{2}

are constants. When

t = 1.25

the deceleration of

P

is

0.5 m/ s^{2}

.

7(a)Kinematics Variable AccelerationMedium4 marks

Find the value of

k_{1}

.

Working

0 words

7(b)Kinematics Variable AccelerationHard5 marks

Given that

P

is only at instantaneous rest when

t = 3.5

, find the distance travelled by

P

in the interval

0 \leq t \leq 1

.

Working

0 words