2023TrialShort answer

Q15 (a) (iii)

2 marks

Question

A particle of unit mass is moving in horizontal motion, subject to a resistance force of $v^2+v^3$ , where $v$ is the object’s velocity. The particle has initial velocity $v_0$ , where $v_0>0$ .

Show that if the particle starts at the origin, then

v=\frac{v_0}{v_0x+v_0t+1}

satisfies the equation of motion.

Try the question before revealing the answer.

Solution

t=-x-\frac1{v_0}+\frac1v\qquad\text{(From iii)}

\frac1v=t+x+\frac1{v_0}

=\frac{v_0t+v_0x+1}{v_0}

v=\frac{v_0}{v_0t+v_0x+1}

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Syllabus alignment

Mechanics

Resisted motionDerive and solve motion models with resistance on horizontal and vertical paths, including terminal velocity.

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