Kinematics

• Choose a positive direction first. Gradient is a rate, area is an accumulation. At the top of a throw, \(v = 0\) but \(a = 9.81\ \mathrm{m\,s^{-2}}\) downwards.
• Positive direction first. Gradient is a rate, area is an accumulation, and area below the axis is negative. At the top, v = 0 but a = 9.81 m s−2 downwards. Projectiles share only the time.

• 2.1.1 I can define — define and use distance, displacement, speed, velocity and acceleration
• 2.1.2 I can use — use graphical methods to represent distance, displacement, speed, velocity and acceleration
• 2.1.3 I can determine — determine displacement from the area under a velocity–time graph
• 2.1.4 I can determine — determine velocity using the gradient of a displacement–time graph
• 2.1.5 I can determine — determine acceleration using the gradient of a velocity–time graph
• 2.1.6 I can — derive, from the definitions of velocity and acceleration, equations that represent uniformly accelerated motion in a straight line
• 2.1.7 I can — solve problems using equations that represent uniformly accelerated motion in a straight line, including the motion of bodies falling in a uniform gravitational field without air resistance
• 2.1.8 I can describe — describe an experiment to determine the acceleration of free fall using a falling object
• 2.1.9 I can describe — describe and explain motion due to a uniform velocity in one direction and a uniform acceleration in a perpendicular direction

The condition travels with the equations. All four equations of motion hold only for constant acceleration in a straight line, or for each component separately in projectile motion. A curved velocity–time graph, or a fall where air resistance matters, is outside them: use the graph instead.

• “At the top of its flight the ball has zero acceleration.” Correct At the top, \(v = 0\) but \(a = 9.81\ \mathrm{m\,s^{-2}}\) downwards, the same as on the way up and on the way down. Zero velocity is not zero acceleration: the velocity is still changing at that instant.
• “The velocity–time graph of a ball thrown up and caught is a V.” Correct That is the speed–time graph. The velocity–time graph is one straight line of gradient \(-9.81\ \mathrm{m\,s^{-2}}\) (upwards positive) that crosses the time axis at the top.
• “The area under a velocity–time graph is the distance travelled.” Correct It is the displacement. Area below the time axis counts as negative. Add the sizes of the areas only when the question asks for distance.
• “Negative acceleration means slowing down.” Correct It means the acceleration points in the negative direction. An object already moving in the negative direction speeds up when its acceleration is negative.
• “All four equations of motion are on the formula sheet.” Correct Only \(s = ut + \tfrac{1}{2}at^2\) and \(v^2 = u^2 + 2as\) are printed. Recall \(v = u + at\) and \(s = \tfrac{1}{2}(u + v)t\), and be able to derive all four.
• “At the top of a projectile's path its velocity is zero.” Correct Only the vertical component is zero. The ball is still moving horizontally at \(u\cos\theta\).
• “Use \(g = 10\ \mathrm{m\,s^{-2}}\) to save time.” Correct Use the Data-sheet value, \(9.81\ \mathrm{m\,s^{-2}}\), unless a question tells you otherwise.
• “Displacement and distance are the same thing.” Repair Distance is the length of path travelled, a scalar. Displacement is the straight-line distance from a reference point in a stated direction, a vector. One lap of a 400 m track: distance 400 m, displacement zero.
• “At the top of its flight the ball's acceleration is zero.” Repair The velocity is zero; the acceleration is still 9.81 m s−2 downwards. If the acceleration were zero there, the ball would stay at the top.
• “The velocity–time graph of a ball thrown up and caught is a V.” Repair That is the speed–time graph. The velocity–time graph is one straight line of constant negative gradient (upwards positive), crossing the time axis at the top.
• “The area under a velocity–time graph is always the distance.” Repair It is the displacement; area below the axis is negative. Add the sizes of the areas only when you want the distance.
• “Negative acceleration means slowing down.” Repair It means the acceleration points in the negative direction. An object moving in the negative direction with a negative acceleration speeds up.
• “Heavier objects fall faster.” Repair Without air resistance every object has the same acceleration, \(g\). Differences you see in air are caused by air resistance, whose effect depends on mass and shape (Topic 3).
• “The velocity at P is the gradient of the line from the origin to P.” Repair On a curved displacement–time graph that chord gives the average velocity. The instantaneous velocity is the gradient of the tangent at P.
• “I used \(v = u + at\) for the ball falling through the air with drag.” Repair The equations of motion need a constant acceleration. With drag the acceleration changes, so they do not apply.
• “\(t = -1.24\ \mathrm{s}\) is also an answer.” Repair Reject a root that lies before the motion began, and say that this is why you reject it.
• “\(v^2 = 686.5\), so \(v = 26.2\ \mathrm{m\,s^{-1}}\).” (for a stone moving downwards, upwards positive) Repair The square root has two signs. Choose from the physics: the stone is moving down, so \(v = -26.2\ \mathrm{m\,s^{-1}}\), that is 26.2 m s−1 downwards.
• “In a projectile the horizontal velocity decreases as the ball rises.” Repair With no air resistance there is no horizontal force, so the horizontal component is constant throughout. Only the vertical component changes.
• “At the top of a projectile's path its velocity is zero.” Repair Only the vertical component is zero. The velocity is \(u_x\), horizontal.
• “The uncertainty in \(t^2\) is the same percentage as in \(t\).” Repair Squaring doubles the percentage uncertainty: 0.5% in \(t\) is 1.0% in \(t^2\).
• “The main source of error was human error.” Repair Name the quantity and the cause: the electromagnet's release delay makes every measured \(t\) too long, so \(g\) comes out too small.

• Read the command word before you decide how much to write. This syllabus has fifteen of them: calculate, comment, compare, define, describe, determine, explain, give, identify, justify, predict, show (that), sketch, state and suggest. Define wants a precise meaning — for a physical quantity, usually an equation in words with every quantity named. State and give want a fact and nothing more. Describe wants the points or the features. Explain wants the reasons and the relationships — a describe-level answer to an explain question is incomplete however well written it is. Show (that) gives you the result and asks for the structured evidence that leads to it, so every step must appear — and a final value worked to one more significant figure than the one printed makes it plain that you calculated it rather than copied it. Sketch wants a freehand graph with its key features — intercepts, asymptotes, the shape — correct, but no plotted scale.
• Read the scales, not the squares. A gradient is (change in the quantity on the \(y\)-axis) ÷ (change in the quantity on the \(x\)-axis), each read from the axis numbers with their units. Counting grid squares gives a number with no unit and usually the wrong size.
• Interleave with the chapters that use this one. Topic 3 (dynamics) supplies the cause of acceleration: re-answer “why is the acceleration at the top of a throw not zero?” with forces. Topic 5 (work, energy and power) turns v2 = u2 + 2as into an energy statement: re-derive a fall speed both ways. Topic 12 (circular motion) is acceleration at constant speed: re-answer “can a body with constant speed accelerate?”. Recalling a topic inside a new context is worth more than another pass over this chapter on its own; at A Level, Paper 4 assumes the whole of the AS content, so nothing here is ever finished with.

• Cambridge International AS & A Level Physics 9702 has five components. Topic 2 is AS Level content, so it is examined in Papers 1, 2 and 3. AS Level content: examined in Paper 1 (multiple choice), Paper 2 (AS structured) and, as practical context, Paper 3. Assumed knowledge for Papers 4 and 5. AS Level candidates take Papers 1, 2 and 3; A Level candidates take all five, either staged over two years (Papers 1–3 in year one, Papers 4 and 5 in year two) or together in one series. Examinations are available in the June and November series, and in March in India.
• Across both the AS Level and the A Level the assessment objectives are weighted AO1 40% (knowledge and understanding), AO2 40% (handling, applying and evaluating information) and AO3 20% (experimental skills and investigations). AS candidates are graded a–e; A Level candidates A*–E. The Data and formulas sheet is printed as page 2 of Papers 1 and 2 and as pages 2 and 3 of Paper 4: it gives the constants and a short list of formulas. Every other equation in this chapter is one the syllabus says you must recall, and this chapter says which is which.
• The outcomes of this topic rest on a handful of distinctions, any one of which a multiple-choice item can turn on: distance or displacement, speed or velocity, zero velocity or zero acceleration, gradient or area, the chord or the tangent. Structured questions can ask you to define the quantities, sketch or describe a motion graph, show that an equation of motion follows from the definitions, and explain projectile motion in terms of independent components.
• Velocities and accelerations read from gradients, displacements from signed areas, and problems solved with the equations of uniformly accelerated motion: free fall with g = 9.81 m s−2, times from the quadratic formula, and projectiles split into components. s = ut + ½at2 and v2 = u2 + 2as are on the Data and formulas sheet; v = u + at and s = ½(u + v)t must be recalled.
• The free-fall experiment: vary the height h (metre rule, to 1 mm), measure the fall time t (an electronic timer started at the release, to 0.001 s), plot h against t2 and take g as twice the gradient. The largest percentage uncertainty is in t2 for the shortest drops; the main systematic error is the electromagnet's release delay. A Paper 5 version analyses v2 against h with error bars.
• Read the command word before you decide how much to write. This syllabus has fifteen of them: calculate, comment, compare, define, describe, determine, explain, give, identify, justify, predict, show (that), sketch, state and suggest. Define wants a precise meaning — for a physical quantity, usually an equation in words with every quantity named. State and give want a fact and nothing more. Describe wants the points or the features. Explain wants the reasons and the relationships — a describe-level answer to an explain question is incomplete however well written it is. Show (that) gives you the result and asks for the structured evidence that leads to it, so every step must appear — and a final value worked to one more significant figure than the one printed makes it plain that you calculated it rather than copied it. Sketch wants a freehand graph with its key features — intercepts, asymptotes, the shape — correct, but no plotted scale.