Motion in One Dimension

Understanding position, velocity, acceleration, and the equations that describe linear motion

Grade 10 Physical Sciences

Key Concept: Kinematics is the study of motion without considering forces. All motion is described using position, displacement, velocity, and acceleration.

Motion Simulator

Watch how the car moves with different velocities

Position: 50 px Velocity: 0 m/s

1. Key Terms & Symbols

Position (x)

Definition: Location relative to a reference point

Type: Vector

Distance (d)

Definition: Total path length traveled

Type: Scalar

Displacement (Δx)

Definition: Change in position (final - initial)

Formula: Δx = x_f - x_i

Velocity (v)

Definition: Rate of change of displacement

Formula: v = Δx/Δt

Acceleration (a)

Definition: Rate of change of velocity

Formula: a = Δv/Δt

Unit: m/s²

2. Equations of Motion

For constant acceleration, these four equations can be used:

v = u + at

u = initial velocity

v = final velocity

a = acceleration

t = time

s = ut + ½at²

s = displacement

u = initial velocity

a = acceleration

t = time

v² = u² + 2as

v = final velocity

u = initial velocity

a = acceleration

s = displacement

s = ½(u + v)t

s = displacement

u = initial velocity

v = final velocity

t = time

Tip: Always establish a positive direction before starting calculations (e.g., right is positive, left is negative). This ensures consistency in your answers.

Equation Solver

Find final velocity (v = u + at)

u (m/s):

a (m/s²):

t (s):

v = 20 m/s

Find displacement (s = ut + ½at²)

u (m/s):

a (m/s²):

t (s):

s = 25 m

3. Graphs of Motion

Position-Time Graph (x vs t)

Slope = Velocity

Steeper slope = higher velocity

Velocity-Time Graph (v vs t)

Slope = Acceleration

Area under graph = Displacement

Acceleration-Time Graph (a vs t)

Horizontal line = Constant acceleration

On a velocity-time graph, what does the slope represent?

4. Instantaneous vs Average Velocity

Average Velocity

v_avg = Δx / Δt

Total displacement divided by total time. Gives an overall picture of motion.

Instantaneous Velocity

Velocity at a specific moment - what a speedometer shows.

Example: A car travels 100 m in 10 seconds. Average velocity = 10 m/s. But the speedometer might show 0 m/s at a red light and 20 m/s on the highway.

Average Velocity Calculator

Initial position (m):

Final position (m):

Time taken (s):

v_avg = 10 m/s

Practice Problem

A car accelerates from rest at 2 m/s² for 5 seconds. What is its final velocity and displacement?

Match the Symbol

Initial velocity

Final velocity

Acceleration

Displacement

Complete the Sentences

The slope of a position-time graph gives .

The area under a velocity-time graph gives .

Acceleration is measured in .

Test Your Understanding

1. Which equation is correct for constant acceleration?

2. A car increases velocity from 10 m/s to 20 m/s in 5 seconds. What is its acceleration?

3. What does a horizontal line on a velocity-time graph mean?

4. Displacement is a:

Key Terms

Position Displacement Distance Velocity Speed Acceleration Initial velocity Final velocity Kinematics Uniform acceleration Position-time graph Velocity-time graph Average velocity Instantaneous velocity

Key Takeaways

Displacement (Δx) = final position - initial position (vector)
Distance is scalar - total path length
Velocity = displacement/time, Acceleration = change in velocity/time
Four equations of motion for constant acceleration: v = u + at, s = ut + ½at², v² = u² + 2as, s = ½(u + v)t
Position-time graph slope = velocity
Velocity-time graph slope = acceleration, area under graph = displacement
Average velocity = total displacement/total time
Instantaneous velocity = velocity at a specific moment
Always choose and state a positive direction before solving problems

Vectors and Scalars Mechanical Energy