Mechanics, Motion, and Energy: JAMB Physics Notes

The equations of motion, Newton's laws, momentum conservation, and work, energy, and power.

Equations of motion (SUVAT)

For constant acceleration, three equations connect initial velocity $u$ , final velocity $v$ , acceleration $a$ , displacement $s$ , and time $t$ : $v = u + a t$ , $s = u t + \frac{1}{2} a t^{2}$ , and $v^{2} = u^{2} + 2 a s$ .

Example 1: A car accelerates uniformly from rest to 20 m/s in 5 s. Find its acceleration and the distance it covers.

$a = \frac{v - u}{t} = \frac{20 - 0}{5} = 4 m / s^{2}$ . $s = u t + \frac{1}{2} a t^{2} = 0 + \frac{1}{2} (4) (25) = 50 m$ .

Newton's laws of motion

Newton's first law: an object stays at rest or moving at constant velocity unless acted on by a resultant force. Newton's second law: $F = ma$ . Newton's third law: every action has an equal and opposite reaction.

Example 2: A resultant force of 15 N acts on a mass of 3 kg. Find its acceleration.

$a = \frac{F}{m} = \frac{15}{3} = 5 m / s^{2}$ .

Momentum and its conservation

Momentum $p = m v$ . In any collision or explosion with no external force, total momentum before equals total momentum after.

Example 3: A 2 kg object moving at 5 m/s collides with, and sticks to, a stationary 3 kg object. Find their common velocity after the collision.

Momentum before $= 2 \times 5 = 10 k g m / s$ . This equals momentum after: $(2 + 3) v = 10$ , so $v = 2 m / s$ .

Work, energy, and power

Work $W = F d$ (force in the direction of motion). Kinetic energy $K E = \frac{1}{2} m v^{2}$ ; gravitational potential energy $P E = m g h$ . Power is the rate of doing work: $P = \frac{W}{t}$ .

Example 4: Find the kinetic energy of a 4 kg object moving at 3 m/s, and the potential energy of a 2 kg object raised 5 m (take $g = 10 m / s^{2}$ ).

$K E = \frac{1}{2} (4) (3^{2}) = 18 J$ . $P E = m g h = 2 \times 10 \times 5 = 100 J$ .

Mechanics, Motion, and Energy

Equations of motion (SUVAT)

Newton's laws of motion

Momentum and its conservation

Work, energy, and power

Key terms

Practise Mechanics, Motion, and Energy questions

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