Acceleration from Velocity-Time Graphs
Read acceleration from the gradient of a velocity-time graph. Signed area gives displacement; adding the magnitudes of areas gives distance travelled. Interpret positive and negative gradients using the sign of velocity, since a negative gradient does not always mean slowing down.
What a learner can do afterwards
- Calculates acceleration as a gradient and quotes it in metres per second squared
- Finds displacement from signed areas and distance travelled from the magnitudes of areas on a velocity-time graph made of straight sections
- Sketches the distance-time graph and the velocity-time graph of the same journey and says how they differ
1 · Read
Acceleration is velocity change per time. Average acceleration = (final velocity - initial velocity) ÷ elapsed time, in m/s². From rest to 12 m/s in 4 s gives 3 m/s². On a straight velocity-time section, this is its constant gradient.
Plot time horizontally and signed velocity vertically. Gradient gives acceleration. A flat line means constant velocity, including rest at zero. A downward slope above zero shows slowing; below zero it shows increasing speed in the negative direction.
Split area into rectangles and triangles, splitting again at zero crossings. Rectangle size = time width × nonnegative velocity height; 8 m/s for 5 s gives 40 m. Triangle size = half × width × nonnegative height, using the magnitude of the velocity difference. For displacement, count below-axis areas negatively. For distance, add all area sizes positively.
Here distance means total distance travelled, not distance from the start. Returning still adds distance. A distance-time gradient gives speed. For constant positive acceleration from rest, distance-time curves upward and gets steeper; velocity-time rises straight. At constant positive velocity, distance-time rises straight and velocity-time is flat. Total distance travelled never decreases.
Gradient gives acceleration. Signed area gives displacement; adding area sizes gives distance. Check velocity's sign before deciding whether speed rises or falls.
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