Velocity-Time graphs – GCSE Mathematics (Higher) OCR Revision

Understanding Velocity-Time Graphs

Velocity: The speed of an object in a particular direction.
Time: The period during which motion takes place.
Initial Velocity: The velocity of an object at t=0.
Final Velocity: The velocity of an object when the motion stops.
Velocity-Time Graph: A graphical representation of an object’s velocity over a period of time.

With Velocity-Time graphs, velocity is shown on the y-axis, and time is shown on the x-axis.
The gradient of a Velocity-Time graph represents the acceleration.
A horizontal line on a Velocity-Time graph represents a constant velocity, showing zero acceleration.
A sloping, linear line shows a constant acceleration. Slope upwards indicates positive acceleration, slope downwards indicates negative acceleration or deceleration.
The area under the graph represents the distance travelled.

To find the acceleration from a Velocity-Time graph, use the formula a = (v - u) / t, where ‘a’ is acceleration, ‘v’ is final velocity, ‘u’ is initial velocity and ‘t’ is time.
To calculate the distance travelled, find the area under the graph. This can be calculated as follows: if the line is horizontal, then distance = speed x time, if the line is a triangle or can be segmented into triangles, then distance = 0.5 x base x height.

A positive acceleration graph shows a line rising to the right.
A negative acceleration or deceleration graph shows a line falling to the right.
A constant velocity graph shows a flat, horizontal line.

Understanding Velocity-Time graphs allows us to predict the motion and displacement of objects in various fields, from rocket science to sports analysis.
This concept is key in physics for describing motion and forces, as well as in mathematics for integrating and understanding graphs.

As with all mathematical topics, it’s critical to practice and comprehend Velocity-Time graphs in varying contexts and real-world applications.