Edexcel IGCSE Math B 4.N kinematics applications

Practise kinematics questions by interpreting distance-time or displacement functions, differentiating where needed and reading speed from gradients.

Exam points

Differentiate displacement functions to find velocity or acceleration at a time.
Use graph gradients to estimate speed from distance-time curves accurately.
Solve kinematics equations involving constants such as k and time t clearly.

[Maximum number: 2]

A particle P is moving along a straight line through the fixed point O.
The speed, v m/s, of P at time t seconds is given by
$v=\frac{t^2}{27}+2+\frac{3}{t^2}$
for $1\leqslant t\leqslant5$ .

The acceleration of P at time t seconds, where $1\leqslant t\leqslant5$ , is a m/s $^2$ .
Find an expression for a in terms of t.

Differentiating:
$a=\frac{2t}{27}-6t^{-3}.$
Final answer:
$a=\frac{2t}{27}-6t^{-3}$

Marking notes:
M1 for attempting to differentiate with one term in t correct. Penalise extra terms.

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4.N Kinematics applications question 1