Distance-time graph

M Joseph Dept. of Science Colyton High School

• We can show the movement of objects by drawing a graph.

speed (m/s) = distance (m) ÷ time (s)

• Speed is the rate of change of distance with time.• The gradient (slope) of the graph gives us speed.• The gradient is given by the change in distance (rise) ÷

time taken (distance along y-axis).

• If the gradient is steeper, the speed is greater. If the graph is curved, it means that the speed of the object is changing.

• The gradient of the graph tells us how the speed is changing.

1. Describe the different motions of the hare and the tortoise, using terms such as distance, speed, time and acceleration. 2. At which points in the story might the hare and tortoise be accelerating or decelerating (that is, under what conditions)? 3. Illustrate the motion of each animal on the same distance–time graph, labelling the changes that occur. 4. Calculate the speed of each animal during the course of the race. 5. If the tortoise travelled the 300 m of the race in a time of 150 seconds, calculate the average speed of its journey (in metres per second). What was the hare’s average speed over the first 30 seconds of its race?

http://www.youtube.com/watch?v=jRwfTW-WdC8&feature=youtu.be

A velocity-time graph for a moving object.

• Describe the motion of the object based on the graph data.

• For example, "What happens to the object after the first 4 seconds?" or "Over the entire time interval, how long is the object stationary?".

A distance-time graph for a moving object.

• Describe the motion of the object based on the graph data.

• For example, "Describe what is happening during the first 3 seconds of measurement." or "Identify areas of the graph where the object is stationary".

A distance-time graph for a moving object.

• Describe the motion of the object based on the graph data.

• For example, "If the distance is measured from a fixed point, with positions to the right as positive, is the object moving to the left or right?".

A distance-time graph for a moving object.

• Describe the motion of the object based on the graph data.

• For example, "Describe what is happening during the first 3 seconds of measurement." or "Identify areas of the graph where the object is stationary".

A distance-time graph for a moving object, showing uniform velocity.

• Describe the motion of the object based on the graph data.

• For example, "Is this object accelerating?".

A distance-time graph for a moving object.

• Describe the motion of the object based on the graph data. • For example, "Describe what is happening during the last 5 seconds of

measurement." or "Identify areas of the graph where the object is stationary".

Distance Time Graph• This graph represents a hike taken by some

students:• What was the distance

travelled after 2 hours?

• What happened from point P to point R?

• Was the students' speed greater during the first part or the second part of the hike?

http://graphaday.blogspot.com/2010/01/distance-time-graph.html

Distance-Time Graph Exercise – Alternative

• We are going on a hike. We start walking and cover a distance of 12 km in 2 hours. Then we stop for a one hour break. We continue our hike by walking for another 2 hours and covering 8 km. Represent this on a distance-time graph.

• As soon as we start walking, the time is zero. Then we walk and cover a distance of 12 km in 2 hours. (Plot line). We stop for a one hour break. (Plot line). Our hike continues by walking for 2 hours covering 8 km. (Plot line). We get the graph beyond.

http://www.deliamalta.com/physics/students'_notes.htm#dis-tim

Distance-Time Graph Exercise

• We are going on a hike. We start walking and cover a distance of 12 km in 2 hours. Then we stop for a one hour break. We continue our hike by walking for another 2 hours and covering 8 km. Represent this on a distance-time graph.

• As soon as we start walking, the time is zero. Then we walk and cover a distance of 12 km in 2 hours. (Plot line). We stop for a one hour break. (Plot line). Our hike continues by walking for 2 hours covering 8 km. (Plot line). We get the graph beyond. http://www.deliamalta.com/physics/students'_notes.htm#dis-tim

Distance–time graphs

Figure 1 A distance–time graph of Lucy’s journey. (Note: time is always on the horizontal axis.)

This distance–time graph below shows part of Lucy’s bicycle ride along the Southbank cycle path. She started off riding at quite a fast constant speed, heading towards Kangaroo Point. After 20 seconds Lucy stopped to check her tyres. After another 10 seconds, she hopped back on her bicycle. Thirty seconds later Lucy stopped at some traffic lights for 20 seconds before accelerating off up the road, reaching her destination 30 seconds later.

From the graph, note the following:

A–B, C–D: A straight sloped line illustrates constant speed. The steeper the line, the greater the speed. Where on the graph is Lucy’s speed the greatest?

B–C, D–E: A horizontal line indicates that Lucy is not moving.

E–F: A curved line indicates that Lucy is not travelling at a constant speed (she is accelerating—either speeding up or slowing down).

1 Use the graph on page 1 to answer the following.

a How fast is Lucy riding during section C–D of her journey?_______________________________________________________________________

b How fast is she riding during section E–F?_______________________________________________________________________

2 What information does a distance–time graph give?_______________________________________________________________________

3 What does a horizontal line above the time axis mean on a distance–time graph? _______________________________________________________________________

4 Use the graph to answer the following.a What is Lucy’s average speed when travelling from B to E?__________________________________________________________

b What is her average speed over the whole trip?___________________________________________________________

5 Describe the motion represented by each of the following distance–time graphs.

Figure 2Distance–time graphs____________________________________________________________________

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