Science · Grades 9–10

Motion & energy · Formula sheet

Rules, conditions and small examples in one printable reference.

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Newton’s second law

Use the net force and consistent SI units for a constant-mass object.

F_net = ma

42 × 13 = 546 N

Acceleration

Velocities include direction; a negative result can represent decreasing positive velocity.

a_avg = (v_f − v_i)/Δt

(-3 − 3)/3 = -2

Displacement at constant velocity

Displacement is signed; distance is the length of the path.

Δx = vΔt

15 × 16 = 240

Kinetic energy

Square speed before multiplying. This is the classical translational kinetic-energy model.

E_k = ½mv²

½ × 8 × 5² = 100

Gravitational potential energy

Height is measured above the chosen reference level. Use the value of g stated in the question.

ΔE_p = mgΔh (constant g)

8 × 10 × 1 = 80

Linear momentum

Momentum has direction; retain the sign of velocity in one dimension.

p = mv

26 × 16 = 416

Mechanical work

For a constant force parallel to displacement, cos θ = 1.

W = Fd cos θ

28 × 34 = 952

Power

One watt is one joule per second.

P_avg = energy transferred / time

192 ÷ 12 = 16

Pressure and force

Force is perpendicular to the surface; pascals are newtons per square metre.

p = F/A

615 ÷ 5 = 123

Thermal energy changes

Assume constant specific heat and no phase change.

Q = mcΔT

12 × 800 × 15 = 144000

Spring force magnitudes

Assume the spring is within its linear elastic range; convert centimetres to metres.

|F| = k|x|

370 × 0.04 = 14.8

Energy efficiency

Useful output cannot exceed total input in this simple energy accounting model.

efficiency % = useful output / input × 100

615/4100 × 100 = 15%