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A-Level Kinematics, uniformly accelerated motion, momentum and Newton's laws
What the A-Level syllabus expects for Kinematics, uniformly accelerated motion, momentum and Newton's laws, and how to practise it.
What the syllabus expects
- Be comfortable with, and make use of, quantities like position, distance, displacement, speed, velocity and acceleration
- Portray distance, displacement, speed, velocity and acceleration by means of graphs
- Read off physical quantities from the slopes of position–time or displacement–time plots, and from both the slopes and enclosed areas of velocity–time plots, even where acceleration varies
- Starting from how velocity and acceleration are defined, obtain the equations that govern straight-line motion at constant acceleration
- Tackle calculations with the constant-acceleration straight-line equations, for instance an object dropping vertically through a uniform gravitational field with drag absent
- Appreciate that a body's mass measures how strongly it opposes any change to its motion
Scope: this reluctance to change is inertia - Give the definition of linear momentum as mass multiplied by velocity, and apply it
- State and use Newton's first law: with no net outside force, whatever is still stays still and whatever moves keeps a steady velocity
- State and use Newton's second law: a body's momentum changes at a rate set in proportion to, and pointing the same way as, the net force on it
- State and use Newton's third law: whenever one object pushes on another, the second pushes back at the same instant with equal strength but reversed direction
- For fixed mass, remember that net force equals ma and deploy this in problems
Scope: F = ma holds only when the mass stays constant
How it's examined
Questions on this topic most often ask you to find, explain, state. About 6% of the past-paper style questions in Rae's bank for this subject sit in this topic.
Worked examples
Example 1 (2 marks)
(a) Explain what an inertial frame of reference is, and state how such a frame is moving.
Show the worked answer
An inertial frame of reference is one in which Newton's first law holds: a body with no resultant force acting on it stays at rest or continues to move in a straight line at constant velocity. Such a frame is not accelerating; it moves with constant velocity (constant speed in a straight line).
Example 2 (3 marks)
At the instant a fully submerged diver has zero horizontal velocity, the viscous drag on him is 950 N upward, the upthrust is 740 N, and his mass is 78 kg. Find the size and direction of his acceleration.
Show the worked answer
Principle: Newton's second law, resultant force F = ma, with the forces first combined as vectors. Take vertically upwards as the positive direction. Step 1 - list every vertical force acting on the diver at that instant. Upthrust from the water, U = 740 N, acting upwards (upthrust always acts upwards). Viscous drag, D = 950 N, acting upwards as stated (drag opposes motion, so the diver must be moving downwards at this instant - consistent with his horizontal velocity being zero). Weight, W = mg, acting downwards, where m = 78 kg and g = 9.81 N kg⁻¹: W = 78 kg × 9.81 N kg⁻¹ W = 765 N. Step 2 - find the resultant by adding the upward forces and subtracting the downward one. F = U + D − W F = 740 N + 950 N − 765 N F = 925 N The answer is positive, so the resultant is 925 N acting vertically upwards. Step 3 - apply Newton's second law. Rearrange F = ma by dividing both sides by m: a = F/m a = 925 N / 78 kg a = 11.9 m s⁻² a ≈ 12 m s⁻². Step 4 - direction. Acceleration is always in the same direction as the resultant force, so the acceleration is 12 m s⁻² directed vertically upwards (the diver is moving downwards but slowing down).
More A-Level H2 Physics topics
Physical quantities, units, measurement uncertainty and vector basics · Types of force, turning effects and conditions for equilibrium · Energy stores and transfers, work, kinetic and potential energy, fields, power and efficiency · Falling freely, the gravitational potential energy of a uniform field, and how air resistance changes the motion · Impulse and the conservation of momentum and energy · Kinematics of uniform circular motion and centripetal acceleration · all of A-Level H2 Physics