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1. Interpreting distance-time graphs

A distance-time graph can be drawn to model the motion of an object moving in a straight line. The gradient of a distance-time graph represents the speed of the object, thus the greater the slope of the graph, the greater the speed of the object.

A straight line in a distance-time graph represents an object moving at a constant speed since the gradient throughout the line stays the same. To find a distance travelled between two particular points on a straight line in the graph, find the difference between the two displacements on the graph. The gradient of a distance-time graph represents the speed of the object whose motion it describes. For objects travelling at a constant speed, this can be calculated using a triangle, whereas for acelerating objects, a tangent can be drawn at the point for which the speed is wanted and the triangle for the tangent line can be used to calculate the speed. # 1

Sketch the distance-time graph of a decelerating (with a decreasing speed) object.

An object that is decelerating has a lower distance-time gradient curve later on.

image # 2

The distance-time graph of an object is given as a straight line. Explain what this says about the speed of the object.

The gradient of the distance-time graph gives the speed of the object. Since the graph is a straight line, the gradient of the graph is constant, therefore the object is travelling at a constant speed.

constant speed # 3

Draw a graph for a car travelling at a constant speed of 12 m/s for the first 10 seconds of its motion.

In 10 seconds the object will travel 12 m/s × 10 s = 120 m.
Thus, the graph can start at 0 s, o m and end at 10 s, 120 m.
Since the speed is constant, the distance-time graph has a straight line.

image # 4

Deduce what is given by the gradient of a distance-time graph modelled by a straight line.

Using the equation for the gradient of a straight line, m = change in y/change in x = distance/time.
This is equivalent to the equation of speed.
Therefore the gradient of a distance-time graph gives the speed of the object.

speed # 5

Draw the graph of an object moving in a straight line at a constant speed and describe shortly what information its gradient gives.

The gradient of a distance-time graph is the speed at which an object is moving. The motion of an object that has a constant speed will be represented by a straight line in the distance-time graph.

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