Describe speed, velocity and acceleration, interpret distance-time and speed-time graphs, and apply Newton's laws and the equation F = ma to simple situations

What this dot point is asking

SEAB wants you to describe motion using speed, velocity and acceleration, to read distance-time and speed-time graphs, and to use Newton's laws together with $F = ma$ to explain and calculate how forces change motion. You also need to know the difference between mass and weight. The calculations stay simple; the marks come from choosing the right equation and quoting units.

The answer

Speed, velocity and acceleration

Speed is how fast something moves, $\text{speed} = \dfrac{\text{distance}}{\text{time}}$. Velocity is speed in a stated direction. Acceleration is the rate of change of velocity:

where $u$ is the starting (initial) velocity and $v$ the final velocity. The unit is $\text{m/s}^2$. A negative acceleration means slowing down (deceleration).

Reading motion graphs

On a distance-time graph the gradient is the speed: a steeper line means faster, a horizontal line means stationary. On a speed-time graph the gradient is the acceleration, and the area under the line is the distance travelled. A horizontal line on a speed-time graph means constant speed (zero acceleration).

Newton's laws

• First law. An object stays at rest or moves at constant velocity unless a resultant force acts on it. This is inertia.
• Second law. A resultant force causes acceleration in the direction of the force, with $F = ma$.
• Third law. When body A pushes on body B, body B pushes back on A with an equal and opposite force.

Mass and weight

Mass is the amount of matter in an object, measured in kilograms, and is the same everywhere. Weight is the gravitational force on that mass, measured in newtons:

where $g$ is the gravitational field strength, about $10\ \text{N/kg}$ on Earth. The same object weighs less on the Moon because $g$ is smaller there, but its mass is unchanged.

Examples in context

Example 1. Seat belts and inertia. When a car stops suddenly, a passenger continues forward because of inertia (Newton's first law). The seat belt provides the backward resultant force that decelerates the passenger safely, spreading the force over the body rather than the head hitting the dashboard.

Example 2. A skydiver reaching terminal velocity. As a falling skydiver speeds up, air resistance grows until it balances the weight. The resultant force becomes zero, so by Newton's first law the acceleration is zero and the skydiver falls at a steady terminal velocity.

Try this

Q1. State Newton's first law of motion. [2 marks]

• Cue. An object remains at rest or continues at constant velocity unless acted on by a resultant (unbalanced) force.

Q2. A $2.0\ \text{kg}$ trolley experiences a resultant force of $6.0\ \text{N}$. Find its acceleration. [2 marks]

• Cue. $a = \dfrac{F}{m} = \dfrac{6.0}{2.0} = 3.0\ \text{m/s}^2$.

Q3. Explain why an astronaut has the same mass but a smaller weight on the Moon. [2 marks]

• Cue. Mass is the amount of matter and does not change; weight is $mg$ and the Moon's $g$ is smaller, so the weight is less.