A student drops a small metal object into a cylinder of oil. The object falls alongside a vertical ruler and a camera records its position at $1.0\text{ s}$ intervals, as shown in Fig. 1.1. (a) On the grid in Fig. 1.2, plot a distance-time graph for the object. (b) The object has a constant speed for some of the time. (i) State and explain how a distance-time graph shows that speed is constant. (ii) Explain, in terms of the forces acting on the object, how it is able to fall…

Physics 5054/22 — May/June 2018

Cambridge O-Level · Theory · worked solutions for every part, with the mark scheme

questions

marks

105

minutes

Topics Kinematics · Forces · Energy, Work and Power · Thermal Properties of Matter · Electromagnetic Induction and Transformers · Practical Electricity · +9 more

Q1KinematicsForcesFree sample

A student drops a small metal object into a cylinder of oil. The object falls alongside a vertical ruler and a camera records its position at $1.0\text{ s}$ intervals, as shown in Fig. 1.1.

Fig. 1.1

(a)

On the grid in Fig. 1.2, plot a distance-time graph for the object.

Fig. 1.2

DifficultyMedium-Easy

Worked solution

Answer

Points plotted at: (1.0, 0.5), (2.0, 1.6), (3.0, 3.0), (4.0, 5.0), (5.0, 7.0).
A smooth curve starting from the origin (0,0) passing through these points, curving upwards and then becoming a straight line.

Final answer

Graph with points at (1, 0.5), (2, 1.6), (3, 3), (4, 5), (5, 7) and a smooth curve from the origin

Detailed explanation

Walkthrough

The question asks to plot a distance-time graph based on the positions shown in Fig. 1.1. We extract the coordinates (time, distance) from the marking scheme (which corrects the image description values to ensure consistency with the final answer):

At $t = 0$ s, distance = 0 cm.
At $t = 1.0$ s, distance = 0.5 cm.
At $t = 2.0$ s, distance = 1.6 cm.
At $t = 3.0$ s, distance = 3.0 cm.
At $t = 4.0$ s, distance = 5.0 cm.
At $t = 5.0$ s, distance = 7.0 cm.

We plot these points on the grid in Fig. 1.2. The horizontal axis is time (0 to 5 s) and the vertical axis is distance (0 to 8 cm). After plotting, we draw a smooth curve connecting the origin to the points. The curve starts steep (high speed) and becomes less steep, eventually becoming a straight line (constant speed).

Key Takeaways

Reading data from a diagram: identify the axis labels and read the values at specific time intervals.
Plotting a graph: ensure points are plotted to within half a small square.
Curve of best fit: for motion with changing speed, draw a smooth curve, not a straight line joining points.

Common Mistakes

Plotting points incorrectly (e.g., swapping time and distance axes).
Drawing straight lines between points instead of a smooth curve.
Forgetting to start the curve at the origin (0,0).

Things to Be Careful About

Read the graph axes carefully: vertical is distance (cm), horizontal is time (s).
The marking scheme specifies specific coordinates (1, 0.5), (2, 1.6), etc. Use these values even if the image description text varies slightly; the marking scheme is the authority for the expected answer.
Plotting precision: points should be plotted to within half a small square on the grid.

Techniques used

read positions from a distance-time apparatus diagramplot a distance-time graph with correct coordinatesdraw a smooth curve of best fit through plotted points

(b)

The object has a constant speed for some of the time.

(i)

State and explain how a distance-time graph shows that speed is constant.

DifficultyMedium-Easy

Worked solution

Answer

The graph is a straight line (or the gradient/slope is constant).
This means the object travels equal distances in equal intervals of time (or the gradient equals speed, which is constant).

Final answer

Straight line (constant gradient); travels equal distances in same time

Detailed explanation

Walkthrough

The question asks how a distance-time graph shows constant speed. Speed is the rate of change of distance, which is the gradient of the distance-time graph ( $v = \Delta d / \Delta t$ ). If the speed is constant, the gradient must be constant. A constant gradient on a graph is represented by a straight line. Alternatively, one can say that for every equal time interval (e.g., every 1 second), the object covers the same distance.

Key Takeaways

Gradient of distance-time graph = speed.
Constant speed = straight line on distance-time graph.
Equal distances in equal time intervals implies constant speed.

Common Mistakes

Saying 'the line is straight' without explaining what that means for the motion.
Confusing distance-time with speed-time graphs (on a speed-time graph, constant speed is a horizontal line; on distance-time, it's a straight sloping line).

Things to Be Careful About

The question asks to 'State and explain'. State the feature (straight line/constant gradient) and explain the consequence (equal distances in same time/constant speed).

Techniques used

interpret the gradient of a distance-time graphrelate constant gradient to constant speed

(ii)

Explain, in terms of the forces acting on the object, how it is able to fall at a constant speed.

DifficultyMedium

Worked solution

Answer

The forces acting are the weight (downwards) and the force from the oil/liquid (upwards) (drag or upthrust).
These forces are balanced (equal and opposite), so there is no resultant force (or resultant force is zero).

Final answer

Weight and upward force from oil are balanced (resultant force is zero)

Detailed explanation

Walkthrough

The object is falling through oil. The forces acting on it are:

Weight acting downwards (due to gravity).
Upward force from the oil. This is a combination of upthrust (buoyancy) and drag (viscous friction). At 5054 level, referring to it as 'force from oil/liquid upwards' or 'drag' is sufficient.

As the object falls, it accelerates initially because weight > upward force. However, as speed increases, the upward drag force increases. Eventually, the upward force equals the weight. At this point, the resultant force is zero. According to Newton's First Law, if the resultant force is zero, the object continues at a constant speed (terminal velocity). The graph in part (a) shows this as the straight-line section where the gradient (speed) is constant.

Key Takeaways

Forces on a falling object in a fluid: Weight (down) and Drag/Upthrust (up).
Constant speed (terminal velocity) occurs when resultant force is zero.
Balanced forces mean no acceleration.

Common Mistakes

Saying 'gravity and air resistance' (it's oil, not air; though air resistance is a type of drag, 'force from oil' is more precise).
Saying 'no forces act' (forces act, they are just balanced).
Confusing mass and weight.

Things to Be Careful About

The question asks 'in terms of the forces acting'. Must name the forces (weight and upward force) and state they are balanced/equal/opposite.
'Resultant force' is a key phrase. 'Forces cancel' is also acceptable.

Techniques used

identify forces acting on a falling object in a fluidapply Newton's first law to constant velocity motionexplain terminal velocity in terms of balanced forces

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