Physics 9702 · AS & A Level · Non-uniform motion

Non-uniform motion — practice question

A child riding on a sledge moves down a steep hill and then continues in a straight path up an ice-covered slope, as shown in Fig. 3.1. The sledge goes past point A with speed $18\,\text{m s}^{-1}$ at time $t = 0$ and later stops at point B. The child then uses a brake on the sledge at point B. The brake is unable to hold the sledge still, so it immediately begins sliding back down the slope towards A. Fig. 3.2 shows how the velocity $v$ of the sledge changes with time $t$ from $t = 0$ to $t = 24\,\text{s}$.
(a)[1]

State the time taken for the sledge to move from A to B.

(b)[3]

Find the displacement of the sledge from point A up the slope at time $t = 24\,\text{s}$.

(c)[2]

Show that the acceleration of the sledge as it moves from B back towards A is $0.50\,\text{m s}^{-2}$.

(d(i))[2]

The combined mass of the child and sledge is $70\,\text{kg}$. The part of their total weight acting down the slope is $80\,\text{N}$. Determine the frictional force on the sledge as it moves from B towards A.

(d(ii))[2]

Determine the angle $\theta$ of the slope to the horizontal.

(d)[4]

The total mass of the child and sledge is $70\,\text{kg}$. The part of the combined weight of the child and sledge that acts down the slope is $80\,\text{N}$. Determine (i) the frictional force on the sledge as it moves from B towards A, and (ii) the angle $\theta$ of the slope to the horizontal.

(e)[3]

Between $t = 4.0\,\text{s}$ and $t = 8.0\,\text{s}$, the child on the sledge sounds a whistle. The whistle produces sound with frequency $900\,\text{Hz}$. The speed of sound in air is $340\,\text{m s}^{-1}$. A man at point A hears the sound. Use Fig. 3.2 to answer the following.

(e(i))[2]

Determine the initial frequency of the sound heard by the man.

(e(ii))[1]

Describe and explain qualitatively any change in the frequency of the sound heard by the man.

Worked solution & mark scheme

This 20-mark question has a full step-by-step worked solution and mark scheme. One marking point: time taken = $12\,\mathrm{s}$

  • Full mark scheme, point by point
  • Step-by-step worked solution
  • Write your answer & get it marked instantly by AI