Graphs of motion in kinematics provide a visual representation of an object’s motion over time. They offer valuable insights into an object’s position, velocity, and acceleration, allowing us to analyze and understand various aspects of its motion.
The graphs of motion for an object released from rest in free fall.
Velocity as gradient of displacement-time graph
Since velocity is defined as the rate of change of displacement, its value can be obtained from the gradient of the tangent of a displacement-time graph.
Acceleration as gradient of velocity-time graph
In the same way, acceleration can be obtained from the gradient of the velocity-time graph.
Displacement as area under velocity-time graph
Conversely, the change in displacement can be obtained from the area under the velocity-time graph. The area referred to is that which is bounded by the line in the graph and the time axis, across the width of duration of change.
If the area is found under the time-axis, the change in displacement is then given a negative sign and is associated with a decrease, as opposed to an increase, in displacement.
Velocity as area under acceleration-time graph
In the same way, change in velocity is obtained from the area under the acceleration-time graph.
Simulation
The simulation below shows the variation in the displacement, velocity and acceleration of an object being projected upwards from the ground. The object begins with a velocity in the upward direction (taken as positive) and experiences a constant downward acceleration throughout until it returns to the original height.
Observe how the graphs change. You can use the sliders to control the time as well as the initial velocity u.