# StudySquare

This page covers the following topics:

1. Speed

2. Typical speed values

3. Average speed

4. Interpreting distance-time graphs

5. Gradient of distance-time graphs

Speed is a scalar quantity, it has a magnitude but no direction. That means that a train that is moving 30 km/h west moves at the same speed as a train that is moving at 30 km/h east.

Speed is usually measured in m/s or km/h, although other compound units may be used. To convert the value of a speed from m/s to km/h, multiply the value by 3.6. To convert speed from km/h to m/s, divide by 3.6.

When describing speed for walking, running and cycling, the speeds will vary due to many factors, such as age, fitness level and the total distance travelled. As age increases, the average typical walking speed of the person decreases. As fitness level increases, the typical average running speed increases.

The typical speed of sound in air is approximately 340 m/s, whereas in a vacuum it is 0 m/s. This is because there are no particles present, which are needed to propagate sound waves, therefore they do not travel in a vacuum.

The equation used to calculate the steady speed of a moving object can also be used to calculate the speed of objects moving at a non-steady speed. The resultant speed is called the average speed and is calculated using the total distance travelled and the time within which it is travelled. For an object not moving at a steady speed, the instantaneous speed cannot be known, since the speed will be different at any point in time during its journey.

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

Anne is running at a speed of 6.5 m/s, while Sumitha is running at a speed of 21.6 km/h. Compare their speeds.

speed of Sumitha = 21.6 ÷ 3.6 = 6 m/s

6.5 m/s > 6 m/s

Anne’s speed is higher.

Anne’s speed is higher.

# 3

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

# 4

Tony is trying to catch a bus by running to a bus stop which is 0.8 km from his house at an average speed of 2.5 m/s. Given that the bus is due to arrive in 2 minutes, decide whether Tony will catch the bus.

Converting the distance to metres, 0.8 km = 800 m.

Converting the time to seconds, 2 minutes = 2 × 60 seconds = 120 s.

Using v = s/t, 2.5 m/s = 800 m/time, time = 320 seconds.

Therefore, Tony won’t get to the bus stop in time to catch the bus.

no

# 5

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

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