CSEC Physics: Distance, Displacement, Speed, Velocity, and Acceleration

On this page, we will explore the fundamental quantities used to describe how objects move: distance, displacement, speed, velocity, and acceleration. Understanding these terms and how they relate to each other is essential for tackling mechanics problems in CSEC Physics.

Distance and Displacement

These two terms are often used interchangeably in everyday language, but in physics, they have different meanings.

  • Distance:
    • Definition: The total length of the path covered by an object during its motion.
    • Type: Scalar quantity (magnitude only).
    • Unit: The standard SI unit is the meter (m). Other units like kilometers (km) and centimeters (cm) are also used.
    • Key Point: Distance only cares about the ground covered, regardless of the direction.
    • Example: If you walk 5 meters East and then 3 meters West, the total distance you covered is 5 m+3 m=8 m.
  • Displacement:
    • Definition: The change in an object’s position in a straight line from its starting point to its ending point. It includes both the magnitude and the direction of this change.
    • Type: Vector quantity (magnitude and direction).
    • Unit: The standard SI unit is the meter (m), along with a specified direction (e.g., m North, m East, m [an angle] from the starting point).
    • Key Point: Displacement is about the overall change in position, taking the direction into account.
    • Example: If you walk 5 meters East and then 3 meters West, your starting point is A and your ending point is B. Your displacement is 5 m (East)−3 m (West)=2 m East. Your final position is 2 meters East of your starting point.

Speed and Velocity

Similarly, speed and velocity are related but different.

  • Speed:
    • Definition: The rate at which an object covers distance. It’s how fast an object is moving, without considering the direction.
    • Type: Scalar quantity (magnitude only).
    • Formula: Speed=Distance​/Time
    • Unit: The standard SI unit is meters per second (m/s). Other common units include kilometers per hour (km/h) and miles per hour (mph).
    • Example: If a car travels a distance of 100 meters in 20 seconds, its speed is 20 s100 m​=5 m/s.
  • Velocity:
    • Definition: The rate at which an object changes its displacement. It’s how fast an object is moving and in what direction.
    • Type: Vector quantity (magnitude and direction).
    • Formula: Velocity=Displacement​/Time
    • Unit: The standard SI unit is meters per second (m/s), along with a specified direction (e.g., m/s North, m/s East).
    • Example: If a car has a displacement of 100 meters East in 20 seconds, its velocity is 20 s100 m East​=5 m/s East.
  • Instantaneous vs. Average: Both speed and velocity can be instantaneous (at a specific moment) or average (over a period of time). The formulas above typically represent average speed and velocity over the given time interval.

Acceleration

Acceleration describes how an object’s velocity changes over time.

  • Acceleration:
    • Definition: The rate of change of velocity. This means either the speed is changing, the direction is changing, or both.
    • Type: Vector quantity (magnitude and direction). The direction of acceleration is the same as the direction of the change in velocity.
    • Formula: Acceleration(a)=Time TakenChange in Velocity​=Time(t)Final Velocity(v)−Initial Velocity(u)​ a=tv−u​
    • Unit: The standard SI unit is meters per second squared (m/s²).
    • Example: If a car starts from rest (initial velocity u=0 m/s) and reaches a velocity of 20 m/s East in 10 seconds, its acceleration is 10 s20 m/s−0 m/s​=2 m/s2 East.
  • Deceleration: This is when an object is slowing down. It’s essentially acceleration in the opposite direction of motion. If an object is moving in the positive direction and decelerating, its acceleration is negative.

Graphs of Motion

Graphs are powerful tools for representing and analyzing motion. For CSEC Physics, you should be familiar with distance-time, displacement-time, speed-time, and velocity-time graphs.

a) Distance-Time Graphs

  • Plots distance traveled against time.
  • The slope (gradient) of a distance-time graph represents speed.
    • A straight line means constant speed.
    • A steeper slope means higher speed.
    • A horizontal line means the object is stationary (speed = 0).
    • The slope is always positive or zero, as distance is a scalar and always increases or stays the same.

b) Displacement-Time Graphs

  • Plots displacement from a reference point against time.
  • The slope (gradient) of a displacement-time graph represents velocity.
    • A straight line means constant velocity.
    • A steeper slope means higher speed in that direction.
    • A horizontal line means the object is stationary (velocity = 0).
    • A positive slope indicates velocity in the positive direction.
    • A negative slope indicates velocity in the negative direction.

c) Speed-Time Graphs

  • Plots speed against time.
  • The slope (gradient) of a speed-time graph represents the magnitude of acceleration (how quickly the speed is changing).
    • A horizontal line means constant speed (acceleration = 0).
    • A straight line with a positive slope means constant acceleration (speed increasing).
    • A straight line with a negative slope means constant deceleration (speed decreasing).
  • The area under a speed-time graph represents the distance traveled.

d) Velocity-Time Graphs

  • Plots velocity against time (taking direction into account – positive and negative values).
  • The slope (gradient) of a velocity-time graph represents acceleration.
    • A horizontal line means constant velocity (acceleration = 0).
    • A straight line with a positive slope means constant acceleration.
    • A straight line with a negative slope means constant acceleration in the opposite direction of motion (deceleration if the velocity and acceleration have opposite signs).
  • The area under a velocity-time graph represents the displacement. Area above the time axis is positive displacement, and area below is negative displacement.

Practice Problems

  1. A runner travels 400 meters around a circular track and finishes at the starting line in 50 seconds.
    • What is the distance covered by the runner?
    • What is the displacement of the runner?
    • What is the average speed of the runner?
    • What is the average velocity of the runner?
  2. A car accelerates from 5 m/s East to 25 m/s East in 4 seconds. What is the acceleration of the car?
  3. A graph shows the velocity of a cyclist over 10 seconds. The velocity increases uniformly from 0 m/s to 15 m/s in the first 6 seconds, then remains constant for the next 4 seconds.
    • Calculate the acceleration of the cyclist during the first 6 seconds.
    • Calculate the displacement of the cyclist during the 10 seconds.