R: Forces and Newton’s laws: Understand and use weight and motion in a straight line under gravity; gravitational acceleration, g , and its value in SI units to varying degrees of accuracy. (The inverse square law for gravitation is not required and g may be assumed to be constant, but students should be aware that g is not a universal constant but depends on location).

The idea

Weight is the force of gravity on a mass: W = mg. Near Earth's surface, g ≈ 9.8 m s⁻², but it varies with location (e.g., 9.81 in UK, 9.78 at equator, 9.83 at poles). For motion in a straight line under gravity alone, use constant acceleration equations (suvat) with a = ±g, taking up as positive or negative consistently. Example: a ball thrown vertically upwards at 20 m s⁻¹: time to highest point t = u/g ≈ 2.04 s, maximum height s = u²/(2g) ≈ 20.4 m. Weight acts downwards; mass is scalar and constant. In SI, g is measured in m s⁻²; use g = 9.8 or 9.81 as required. Remember g is not universal; it depends on planet and altitude.

What earns the marks

• Weight is calculated as W = mg, where m is mass in kg and g is gravitational acceleration in m s⁻²; weight is a force in newtons.
• For vertical motion under gravity, use constant acceleration equations with a = g downwards (or -g if upwards is positive).
• At maximum height, vertical velocity is zero; time to highest point is u/g (if upwards positive).
• g varies with location: approximately 9.81 m s⁻² in the UK, but lower at the equator and higher at the poles; it is not a universal constant.
• When solving problems, state the value of g used and its direction; keep sign conventions consistent throughout.

Common mistakes and how to put them right

• Confusing mass and weight.

  Put it right: Use W = mg for weight and state units clearly.

• Using g = 9.8 m s⁻² but treating it as positive when the object is moving upwards.

  Put it right: Choose a positive direction and apply signs consistently; if upwards is positive, acceleration is -g.

• Assuming g is the same everywhere on Earth.

  Put it right: Recognise that g varies slightly with latitude and altitude; use the value given in the question or standard 9.81 m s⁻² unless told otherwise.

Exam tips

• Always write down the suvat equation you are using and substitute values with correct signs; this gains method marks even if arithmetic slips.
• If a question gives g to a specific accuracy (e.g., 9.8 or 9.81), use that value; do not default to 9.81 if told otherwise.
• For multi-stage vertical motion (e.g., up then down), split the motion into stages and treat each with consistent sign conventions.