Motion

Understanding the concepts of speed, velocity, and acceleration is crucial to describing how objects move. This section will explain these key ideas, provide the relevant formulas, and show how to interpret graphs that represent motion.

Speed and velocity

(a) Speed:

• Speed is defined as the distance travelled per unit time. It is a scalar quantity, meaning it has only magnitude (how fast something is moving) but no direction.

• The formula for speed is:

• Where:

  • v is the speed (in meters per second, m/s).

  • s is the distance travelled (in meters, m).

  • t is the time taken (in seconds, s).

(b) Velocity:

• Velocity is the speed in a given direction. It is a vector quantity, meaning it has both magnitude and direction.

• The average velocity is calculated as:

Distance-time and speed-time graphs

Graphs are useful tools for representing the motion of objects. Two common types of graphs used in physics are distance-time graphs and speed-time graphs.

(a) Distance-Time Graphs:

• These graphs show how the distance travelled by an object changes over time.

• A horizontal line indicates the object is at rest (not moving).

• A straight, sloping line indicates constant speed.

• A curved line indicates acceleration or deceleration.

A distance-time graph.

(b) Speed-Time Graphs:

• These graphs show how the speed of an object changes over time.

• A horizontal line indicates that the object is moving at a constant speed.

• A sloping line indicates acceleration (speed increasing) or deceleration (speed decreasing).

A speed-time graph.

Calculations using graphs

• Speed from Distance-Time Graph:

  • The gradient (slope) of a straight-line section of a distance-time graph gives the speed of the object.

• Distance from Speed-Time Graph:

  • The area under a speed-time graph represents the distance travelled. This is particularly useful for objects moving at a constant speed or with constant acceleration.

Acceleration

(a) Defining Acceleration:

• Acceleration is the change in velocity per unit time. It is a vector quantity.

• The formula for acceleration is:

• Where:

  • a is the acceleration (in meters per second squared, m/s²).

  • Δv is the change in velocity (in m/s).

  • Δt is the time taken for the change (in s).

(b) Constant vs. Changing Acceleration:

• Constant Acceleration: The object's velocity changes at a steady rate, resulting in a straight, sloping line on a speed-time graph.

• Changing Acceleration: The rate of change of velocity varies, resulting in a curved line on the graph.

(c) Deceleration:

• Deceleration is simply negative acceleration. It occurs when an object's velocity decreases over time. It is represented by a downward slope on a speed-time graph.

The gradient of a speed-time graph gives the acceleration of the object.

Acceleration due to gravity

The acceleration of free fall near the surface of the Earth is approximately 9.8 m/s². This value is represented by g and is the same for all objects, regardless of their mass, assuming no air resistance.

Motion in a gravitational field

When objects fall in a uniform gravitational field:

• Without Air Resistance: Objects accelerate at 9.8 m/s² until they hit the ground.

• With Air Resistance: As the object falls, air resistance increases until it balances the weight of the object. At this point, the object reaches terminal velocity and continues to fall at a constant speed.

Circular motion