Distance–time and velocity–time graphs · GCSE Physics

Distance–time graphs

The gradient of a distance–time graph gives the speed.
A straight, sloping line means a constant speed; a steeper line means a faster speed.
A horizontal line means the object is stationary.
A curve that gets steeper means the object is accelerating. (Higher) The speed at any point is the gradient of a tangent to the curve.

The gradient of a velocity–time graph gives the acceleration.
A horizontal line means a constant velocity; a line sloping upwards means acceleration; a line sloping downwards means deceleration.
(Higher) The area under a velocity–time graph gives the distance travelled (displacement).
Count squares or split the area into triangles and rectangles to find it.

An object falling through a fluid, such as a skydiver, first accelerates because of the force of gravity.
As it speeds up, the frictional force (air resistance) increases, so the resultant force and the acceleration decrease.
Eventually the resultant force is zero and the object moves at a constant speed: its terminal velocity.
On a velocity–time graph this shows as a curve that levels off.

Always check the axes: a line going up on a distance–time graph (moving) means something different from one going up on a velocity–time graph (accelerating).
Include units when you give a gradient: m/s for speed and m/s² for acceleration.

Distance–time graph: A graph of distance against time; its gradient is speed.
Velocity–time graph: A graph of velocity against time; its gradient is acceleration.
Gradient: The steepness of a line: change in y ÷ change in x.
Tangent: A straight line touching a curve at a point, used to find the gradient there.
Terminal velocity: The constant maximum velocity of a falling object, when the resultant force is zero.
Stationary: Not moving.