Velocity Time Graphs – GCSE Maths

Practice Questions
Downloads

Introduction

  • A Velocity-Time Graph is a graphical representation that shows how the object’s velocity changes over time.
  • This Graphical Representation is used to analyzing the Motion.

Real-life Scenario:

  • A racer starts from rest, speeds up, moves at a steady pace, then slows down to stop.

A motocross rider mid-air on a dirt bike, symbolizing changing velocity for a velocity-time graph illustration

  • A Ball Dropped from Rest

Silhouette of a basketball player shooting at sunset, capturing projectile motion for velocity-time graph demonstration

What is a Velocity-Time Graph?

  • It is a graphical representation of an object’s motion, which tells us the acceleration of the object.
  • Acceleration of the object depends upon the different types of velocities.

Velocity-time graph with increasing, constant, curved acceleration, and deceleration phases

Features of a Distance-Time Graph:

  • X-axis (Horizontal) → Represents Time (seconds, minutes, hours).
  • Y-axis (Vertical) → Represents Velocity (usually in m/s).
  • Slope of the Graph → Represents Acceleration.
  • Area Under the Graph→ Represents Displacement.

Different types of Slopes in Velocity-Time Graph

  • In Velocity-Time Graph, the Gradient of the line at any point represent the rate of change of velocity with respect to time, which is acceleration.

Gradient equals change in velocity divided by change in time equals acceleration

  • Depending on the slope’s direction and steepness, we can determine whether the object is accelerating or decelerating.

Types of Slopes:

Two velocity-time graphs showing constant velocity for stationary object and constant acceleration for positive slope

Two velocity-time graphs showing constant deceleration and varying acceleration with curved slope

How to Calculate Acceleration from Velocity-Time Graph?

  • Acceleration is the rate of change of velocity over time

To Calculate Acceleration from Velocity-Time Graph follow the steps:

  • Step#1: Understand the graph
  • Step#2: Identify the two points.
  • Step#3: Use the Slope formula,

acceleration formula

Where:

    • a = acceleration (m/s2)
    • Δv = change in velocity (v − u)
    • Δt = time taken (s)
  • Step#4: Calculate the Acceleration.
  • Step#5: Interpret the Result:
    • If Acceleration is zero, then the velocity is constant.
    • If Acceleration is positive, then the object is speeding up.
    • If Acceleration is negative (Deceleration), then the object is slowing down.

certified Physics and Maths tutorSolved Example

Problem: A car accelerates uniformly from rest. Its Velocity-Time Graph is a straight line passing through:

Velocity-time graph with velocity increasing from 10 to 30 over 10 seconds

Find the Acceleration.

Solution: 

Step #1: Given:

    • Initial Time: 0s F
    • inal Time: 10s
    • Initial Velocity: 0m/s
    • Final Velocity: 30m/s

Step #2: Using the Formula:

acceleration formula

Step #3: Putting the values:

Equation showing acceleration calculation using change in velocity over time with values 30 and 10

Acceleration is 3 m/s2

Final Answer: 3 m/s2

How to Calculate Distance from Velocity-Time Graph?

  • Distance is the total length of the path traveled by an object is represented by the area under the graph between two-time intervals.

To Calculate Distance from Velocity-Time Graph follow the steps:

  • Step#1: Understand the graph.
  • Step#2: Use the Area Under the Graph.
  • Step#3: Calculate the Area
    • For a rectangle Area:

Area equals base times height equals time times velocity formula

    • For a triangle Area:

Formula showing area under a velocity-time graph equals 1/2 times time times velocity change

    • For a trapezium Area:

Area equals one-half times sum of parallel sides times height trapezium formula

  • Step#4: Sum up the areas, if it is dividing into section.
  • Step#5: Calculate the Total Distance.

certified Physics and Maths tutorSolved Example

Problem: If a Truck moving with Velocity-Time Graph consisting of:

Velocity-time graph showing velocity increasing to 3 and remaining constant from time 2 to 3 seconds

Find the Distance travelled by the Truck.

Solution: 

Step #1: Understand the graph.

    • The Slope of a Graph divided into two sections a triangle and a rectangle.

Step #2: Calculate the Area:

Area of Triangle:

Triangle area formula used with time and velocity change values

Area of Rectangle:

Area under a velocity-time graph calculated using rectangle formula

Step #3: Sum up the Areas:

Area under a velocity-time graph calculated by adding triangle and rectangle areas

Total Distance Travelled by the Truck is 6m

Final Answer: 6m

Frequently Asked Questions

Solution:

Use the slope of the line.

Acceleration equals change in velocity divided by change in time formula from velocity-time graph

Solution:

Use the Area under the graph — either Rectangle, Triangle, or a combination.

Solution: 

  • Velocity-Time Graph shows velocity change;

its slope = Acceleration.

  • Acceleration-Time Graph shows how acceleration changes;

its area = Velocity change.

Solution:

A negative slope means the object is Decelerating — its Velocity is decreasing over time.

Solution:

It means the object is moving in the opposite direction. The Velocity is negative, but the object is still in Motion.

Solution:

Yes. For example, when an object changes direction at the top of its path (like a ball thrown upward), its velocity is zero for a moment, but it’s still Accelerating due to Gravity.

Request for Demo Lesson

Table of Content