Velocity Time Graphs – GCSE Maths
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 Ball Dropped from Rest
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.
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.
- Depending on the slope’s direction and steepness, we can determine whether the object is accelerating or decelerating.
Types of Slopes:
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,
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.
Solved Example
Solved ExampleProblem: A car accelerates uniformly from rest. Its Velocity-Time Graph is a straight line passing through:
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:
Step #3: Putting the values:
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:
- For a triangle Area:
- For a trapezium Area:
- Step#4: Sum up the areas, if it is dividing into section.
- Step#5: Calculate the Total Distance.
Solved Example
Problem: If a Truck moving with Velocity-Time Graph consisting of:
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:
Area of Rectangle:
Step #3: Sum up the Areas:
Total Distance Travelled by the Truck is 6m
Final Answer: 6m
Frequently Asked Questions
Solution:
Use the slope of the line.
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.