How To Find Acceleration From Distance Time Graph

Describing motion - AQA

The move of objects can be described using motility graphs and numerical values. These are both used to aid in the design of faster and more than efficient vehicles.

Distance-fourth dimension graphs

If an object moves along a straight line, the altitude travelled can be represented past a distance-time graph.

In a distance-fourth dimension graph, the gradient of the line is equal to the speed of the object. The greater the gradient (and the steeper the line) the faster the object is moving.

A distance time graph shows distance travelled measured by time.

Instance

Summate the speed of the object represented by the green line in the graph, from 0 to iv s.

modify in distance = (8 - 0) = viii m

change in time = (4 - 0) = 4 due south

\[speed = \frac{distance}{fourth dimension}\]

\[speed = 8 \div 4\]

\[speed = 2~g/s\]

Question

Summate the speed of the object represented by the purple line in the graph.

change in distance = (x - 0) = 10 m

alter in fourth dimension = (two - 0) = two southward

\[speed = \frac{distance}{time}\]

\[speed = 10 \div ii\]

\[speed = 5~1000/due south\]

The speed of an object can be calculated from the gradient of a distance-time graph.

Distance-time graphs for accelerating objects - Higher

If the speed of an object changes, information technology will be accelerating or decelerating . This tin can be shown equally a curved line on a distance-fourth dimension graph.

A graph to show distance travelled by time. A shows acceleration, B shows constant speed, C shows deceleration, and A shows stationary position. Three dotted lines separate each section.

The table shows what each department of the graph represents:

Section of graph	Gradient	Speed
A	Increasing	Increasing
B	Constant	Abiding
C	Decreasing	Decreasing
D	Zero	Stationary (at rest)

If an object is accelerating or decelerating, its speed tin be calculated at any detail fourth dimension by:

drawing a tangent to the bend at that time
measuring the gradient of the tangent

A distance x time graph, showing a tangent on a curve.

Every bit the diagram shows, afterwards drawing the tangent, work out the modify in distance (A) and the change in time (B).

\[gradient = \frac{vertical~change (A)}{horizontal~alter (B)}\]

It should also exist noted that an object moving at a abiding speed but changing direction continually is also accelerating. Velocity , a vector quantity, changes if either the magnitude or the management changes. This is important when dealing with circular motion.