All subjects · Physics · WPH11 (Unit 1)

Newton's first and second laws

Newton's laws connect forces to motion. The second law, ΣF = ma, is used in nearly every mechanics question.

Newton's first law

An object stays at rest or moves at constant velocity unless a resultant force acts on it. This is the special case of ΣF = ma with a = 0: balanced forces mean no acceleration, not necessarily no motion.

Newton's second law

ΣF = ma. The resultant force (vector sum of all forces) in newtons equals mass in kg times acceleration in m/s2. The acceleration is in the direction of the resultant force. Find the resultant first, then divide by mass.

Weight and g

Weight W = mg. g is the gravitational field strength, g = F / m, the force per unit mass: 9.81 N/kg near the Earth's surface, which equals the free-fall acceleration 9.81 m/s2.

Terminal velocity

When an object falls through a fluid, drag grows as speed increases. The resultant force (W - drag) falls, so acceleration falls. When drag equals weight (minus any upthrust), the resultant force is zero and the object moves at a constant terminal velocity.

Worked example

A 1200 kg car has a driving force of 3000 N and resistive forces of 600 N. Find its acceleration.

  1. ΣF = 3000 - 600 = 2400 N
  2. a = ΣF / m = 2400 / 1200

Answer: a = 2.0 m/s2

Key idea: ΣF = ma with the resultant force; W = mg with g = 9.81 N/kg; zero resultant means constant velocity.

Check yourself

  1. Find the weight of a 65 kg student on Earth, in N, to 3 s.f.
    Show answer

    638 N. W = mg = 65 x 9.81 = 638 N.

  2. A resultant force of 15 N acts on a 3.0 kg mass. Find its acceleration in m/s2.
    Show answer

    5 m/s2. a = F / m = 15 / 3.0 = 5.0 m/s2.

  3. A 2.0 kg model rocket has an upward thrust of 30 N. Find its upward acceleration in m/s2, to 3 s.f.
    Show answer

    5.19 m/s2. Weight = 19.62 N; ΣF = 30 - 19.62 = 10.38 N; a = 10.38 / 2.0 = 5.19 m/s2.

  4. An object moves in a straight line at constant velocity. What is the resultant force on it?
    • Equal to its weight
    • In the direction of motion
    • Opposite to the direction of motion
    • Zero
    Show answer

    Zero. Constant velocity means a = 0, so ΣF = 0 (Newton's first law).

  5. Why does a falling object eventually reach terminal velocity?
    • Gravity becomes weaker as it falls
    • Drag increases with speed until it balances the weight
    • Its mass decreases
    • Drag is always equal to weight
    Show answer

    Drag increases with speed until it balances the weight. As speed rises, drag rises, until the resultant force becomes zero.

  6. A lift of mass 800 kg accelerates upwards at 0.50 m/s2. Find the tension in its cable in N, to 3 s.f.
    Show answer

    8250 N. T - mg = ma, so T = 800 x (9.81 + 0.50) = 8250 N.

  7. A 2.0 kg mass has a weight of 3.2 N on the Moon. Find the gravitational field strength there in N/kg.
    Show answer

    1.6 N/kg. g = F / m = 3.2 / 2.0 = 1.6 N/kg.

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Last updated 7 November 2026. Spotted a mistake? Tell us.