Linear motion — OCR A-Level Physics
Test yourself on Linear motion with OCR A-Level practice questions.
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Linear motion explained
This row is a guided-reading pointer within section 3.1.2 Linear motion.
Read the full explanation
It signals that the learner should read the specification statements that follow, beginning with the equations of motion for constant acceleration in a straight line and the techniques used to investigate motion and collisions. The learner should identify the key quantities: initial velocity u, final velocity v, acceleration a, displacement s and time t, and note that the equations apply only when acceleration is constant and motion is in a straight line. The learner should also note the practical context of investigating motion and collisions, and prepare to connect the equations to measurements such as light gates, ticker timers or video analysis. No numerical values or fixed mark allocations are implied by this pointer.
(i) the equations of motion for constant acceleration in a straight line, including motion of bodies falling in a uniform gravitational field without air resistance: v = u + at, s = 1/2(u + v)t, s = ut + 1/2 at², v² = u² + 2as
For constant acceleration in a straight line, four equations link initial velocity u, final velocity v, acceleration a, displacement s and time t: v = u + at, s = 1/2(u + v)t, s = ut + 1/2 at², and v² = u² + 2as. Each equation omits one quantity, so choose the one that matches the data and the unknown. For a body falling in a uniform gravitational field without air resistance, take a = g, approximately 9.81 m s⁻² downwards, and define a positive direction consistently. For example, a ball dropped from rest for 2.0 s has v = 0 + 9.81 × 2.0 = 19.62 m s⁻¹ and s = 0 × 2.0 + 1/2 × 9.81 × (2.0)² = 19.62 m. Always check units and the sign of each vector.
(ii) techniques and procedures used to investigate the motion and collisions of objects
Investigating motion and collisions involves measuring time, displacement and velocity, then using the equations of motion or conservation laws to analyse the results. Typical techniques include light gates to measure speed, ticker timers or video analysis to record position against time, and apparatus such as a linear air track or dynamics trolleys to reduce friction during collisions. For a collision, measure masses and velocities before and after, and compare total momentum to test conservation. For example, two trolleys on a track can be timed through light gates before and after colliding; the measured velocities and masses allow momentum to be calculated. Procedures must control variables, repeat readings and reduce random and systematic errors.
(b)
This section focuses on the equations of motion for constant acceleration, commonly known as the 'suvat' equations. These relate displacement ($s$), initial velocity ($u$), final velocity ($v$), acceleration ($a$), and time ($t$). The four key equations are $v = u + at$, $s = \frac{1}{2}(u+v)t$, $s = ut + \frac{1}{2}at^2$, and $v^2 = u^2 + 2as$. When reading your textbook, ensure you can select the correct equation based on the known and unknown variables. Pay close attention to vector directions; for example, if an object is thrown upwards, acceleration due to gravity ($g = 9.81 \text{ m s}^{-2}$) acts downwards, so you must assign consistent positive and negative signs to $u$, $v$, $s$, and $a$. Practice applying these equations to scenarios like free fall.
(i) acceleration g of free fall
Free fall means motion under gravity alone, with air resistance negligible. Near the Earth's surface the acceleration is g, approximately 9.81 m s⁻², directed downwards. Because g is constant, the equations of motion apply: for a dropped object starting from rest, v = gt and s = ½gt², so a fall of 4.9 m takes about 1.0 s. Note that g is an acceleration, not a force or a speed, and its unit is m s⁻². All objects fall with the same g in the absence of air resistance, which is why a feather and a coin match in a vacuum. In multiple-choice questions, check whether the object starts from rest, whether upward is taken as positive, and whether the value quoted is g or a multiple of it.
(ii) techniques and procedures used to determine the acceleration of free fall, to include using trapdoor and electromagnet arrangement and light gates and timer arrangement
Two standard laboratory methods determine g. In the trapdoor and electromagnet arrangement, a steel ball is held by an electromagnet; when the current is switched off the ball falls and, on reaching the trapdoor, breaks a circuit and stops a timer. The measured time t and fall height s give g from s = ½gt², so g = 2s/t². In the light-gate arrangement, a card of known length passes through a gate (or two gates a known distance apart) and the timer records the interruption, giving speed and hence acceleration. Both methods reduce timing error by removing human reaction time. Repeat readings, measure s carefully and plot a suitable graph, such as s against t², whose gradient gives ½g.
(c) reaction time and thinking distance; braking distance and stopping distance for a vehicle.
Stopping distance is the total distance a vehicle travels from the moment the driver needs to stop until it is at rest. It has two parts. Thinking distance is the distance travelled during the driver's reaction time, before the brakes are applied; it equals speed multiplied by reaction time, so it grows with speed and with a slower reaction. Braking distance is the distance travelled while the brakes are applied, and it depends on the braking force, the mass of the vehicle and the road conditions. Stopping distance is the sum of the two. Because thinking distance is proportional to speed and braking distance depends on the square of speed, stopping distance rises steeply as speed increases.
Your focus
- Identify the quantities and conditions involved in the equations of motion for constant acceleration.
- Describe how practical techniques are used to investigate motion and collisions.
- Select the appropriate equation or method for a given linear-motion scenario.
Show all 21 objectives
- Select and apply the correct equation of motion for a constant-acceleration problem.
- Solve problems involving bodies falling in a uniform gravitational field without air resistance.
- Use consistent sign conventions and units when substituting into the equations of motion.
- Describe techniques used to measure motion, such as light gates and video analysis.
- Explain how to investigate collisions and test conservation of momentum.
- Evaluate procedures for controlling variables and reducing errors.
- State the four equations of motion for constant acceleration.
- Select the appropriate equation of motion to solve a problem based on the given variables.
- Apply consistent sign conventions for displacement, velocity, and acceleration in one-dimensional motion.
- State the value and direction of the acceleration of free fall near the Earth's surface.
- Apply v = gt and s = ½gt² to an object released from rest.
- Explain why all bodies fall with the same acceleration when air resistance is negligible.
- Describe the trapdoor and electromagnet procedure for measuring g.
- Describe how light gates and a timer are used to find acceleration.
- Explain how repeating readings and plotting a graph improve the accuracy of the result.
- Define thinking distance, braking distance and stopping distance.
- Calculate thinking distance from speed and reaction time.
- Explain how stopping distance changes as speed increases.
Linear motion exam tips
Marking Points
- The equation v = u + at links final velocity, initial velocity, acceleration and time, and is used when displacement is not required.
- The equation s = 1/2(u + v)t links displacement, initial and final velocities and time, and is used when acceleration is not required.
- The equation s = ut + 1/2 at² links displacement, initial velocity, acceleration and time, and is used when final velocity is not required.
- The equation v² = u² + 2as links final velocity, initial velocity, acceleration and displacement, and is used when time is not required.
- For a body falling in a uniform gravitational field without air resistance, acceleration is g, approximately 9.81 m s⁻², and a consistent positive direction must be chosen.
- Light gates measure the time for an object to pass and, with a known length, allow speed or velocity to be calculated.
- Ticker timers or video analysis record position at known time intervals, allowing displacement–time and velocity–time data to be produced.
- A linear air track or low-friction trolley system reduces friction so that motion and collisions approximate ideal conditions.
- For collisions, masses and velocities before and after are measured so that total momentum can be calculated and conservation tested.
- Repeating readings and controlling variables improve reliability and help identify random and systematic errors.
- g is the acceleration of a body in free fall, equal to about 9.81 m s⁻² near the Earth's surface.
- g is directed vertically downwards and is treated as constant over the distances considered at this level.
- In the absence of air resistance, all bodies fall with the same acceleration g regardless of mass.
- For an object released from rest, v = gt and s = ½gt² follow directly from the equations of motion with a = g.
- Trapdoor and electromagnet method: the electromagnet releases a steel ball and the trapdoor stops a timer, so g = 2s/t² from s = ½gt².
- Light gates and timer method: a card of measured length passing through a gate gives speed, and two gates a known distance apart give acceleration.
- Both methods remove human reaction time from the measurement, which is their main advantage over hand timing.
- Repeating readings and plotting a graph such as s against t², with gradient ½g, reduces random error and improves the value of g.
- Thinking distance is the distance travelled during the driver's reaction time, before the brakes are applied.
- Thinking distance equals speed multiplied by reaction time, so it increases with speed and with a longer reaction time.
- Braking distance is the distance travelled while the brakes are applied, and it depends on braking force, vehicle mass and road conditions.
- Stopping distance is the sum of thinking distance and braking distance, and it increases more than proportionally with speed.
Examiner Tips
- 💡Read the full section 3.1.2 statements before attempting questions, and list the symbols and units for each quantity.
- 💡Link each equation of motion to a graph or practical method so you can choose the right approach in an exam question.
- 💡Check whether a question describes constant acceleration or a changing acceleration before selecting an equation.
- 💡List the known quantities with their symbols and units, then choose the equation that contains the unknown and the knowns.
- 💡Define a positive direction before substituting, especially for falling bodies, and keep the sign of g consistent.
- 💡Substitute values only after rearranging the equation, and check that the final unit matches the quantity required.
- 💡State the apparatus and the quantity it measures, and explain how the measurement is converted into velocity or momentum.
- 💡Describe how variables are controlled and how repeats improve reliability.
- 💡For collision questions, identify the before and after states and check whether momentum is conserved.
- 💡Always list the known 'suvat' variables with their signs before choosing which equation to use.
- 💡Remember that for an object dropped from rest, $u = 0 \text{ m s}^{-1}$, and at the maximum height of a vertical throw, $v = 0 \text{ m s}^{-1}$.
- 💡Check your units; ensure time is in seconds, displacement in metres, and velocity in $\text{m s}^{-1}$ before calculating.
- 💡Check the unit in each option: an acceleration must be in m s⁻², so any answer in m s⁻¹ or N can be eliminated immediately.
- 💡Decide your positive direction before substituting into an equation, and keep the sign of g consistent with it.
- 💡For a dropped object, remember the initial velocity is zero, which simplifies v = gt and s = ½gt².
- 💡Identify which quantity each method measures directly: the trapdoor method gives a time for a known distance, while light gates give speeds at known positions.
- 💡When a graph is plotted, state what the gradient represents before using it, for example gradient of s against t² equals ½g.
- 💡Mention repeats and averaging whenever a question asks how to improve the accuracy of a g determination.
- 💡Write the relationship as stopping distance = thinking distance + braking distance before substituting any values.
- 💡Check whether a question gives reaction time or asks you to find it; thinking distance divided by speed gives reaction time.
- 💡When comparing two speeds, remember that doubling the speed doubles thinking distance but roughly quadruples braking distance.
Common Mistakes
- Treating the pointer as a standalone fact to memorise: the correction is to use it to locate and read the following specification statements in full.
- Assuming the equations of motion apply to any motion: the correction is to check that acceleration is constant and motion is in a straight line before using them.
- Skipping the practical techniques because they look less mathematical: the correction is to study how motion and collisions are investigated, including the measurements and apparatus involved.
- Using an equation that contains the unknown quantity: the error is choosing an equation that includes both the required unknown and an unmeasured quantity; the correction is to select the equation that omits the unmeasured quantity.
- Forgetting that the equations apply only for constant acceleration in a straight line: the error is applying them to changing acceleration or curved motion; the correction is to check the conditions first.
- Mixing up u and v or omitting a sign: the error is substituting initial velocity for final velocity or ignoring direction; the correction is to define a positive direction and label u and v carefully.
- Using g = 9.81 m s⁻² without direction or with the wrong sign: the error is treating g as a positive scalar in every case; the correction is to assign the sign of g according to the chosen positive direction.
- Using a single measurement without repeats: the error is treating one reading as reliable; the correction is to repeat and average readings to reduce random error.
- Ignoring friction or air resistance: the error is assuming ideal motion when friction is significant; the correction is to use low-friction apparatus or account for the effect.
- Measuring speed with a stopwatch over a short distance: the error is large reaction-time uncertainty; the correction is to use light gates or a longer distance to improve precision.
- Failing to measure mass in a collision experiment: the error is comparing velocities only; the correction is to measure mass as well so that momentum can be calculated.
- Forgetting that the equations of motion only apply when acceleration is constant.
- Mixing up positive and negative directions for vectors, such as failing to make $g$ negative when initial velocity is upwards.
- Using the wrong equation because a variable that is not given and not required was included in the chosen formula.
- Confusing g with the gravitational force or weight; g is an acceleration in m s⁻², whereas weight is a force in N.
- Believing heavier objects fall faster; in the absence of air resistance all bodies have the same acceleration g.
- Using g = 9.81 m s⁻² with the wrong sign or direction; choose a positive direction and apply it consistently to displacement, velocity and acceleration.
- Rearranging s = ½gt² incorrectly; the correct form is g = 2s/t², so forgetting the factor of 2 halves the value obtained.
- Assuming the timer starts when the ball is released; in the trapdoor arrangement the timer starts when the electromagnet circuit is broken, so the release and the start are simultaneous.
- Ignoring the finite size of the falling object or card; the measured distance must correspond to the actual fall or the card length used to find speed.
- Confusing thinking distance with braking distance; thinking distance occurs before the brakes act, while braking distance occurs while they act.
- Assuming stopping distance is proportional to speed; thinking distance is proportional to speed but braking distance depends on speed squared, so the total rises steeply.
- Forgetting that reaction time varies with the driver's state, such as tiredness or alcohol, which changes thinking distance without changing the braking system.