Question

plotting and interpreting distance - time graphs

1. each sentence in the table describes one of the graphs shown below. write the letter of the correct graph next to each sentence.

leave home and travel at a constant speed.
leave home, travel at a constant speed, stop for a short time and then return home.
leave home, travel to destination and immediately return.
leave home, travel at a constant speed, stop for some time and then continue journey away from home.

graph a: distance from home vs time (a straight line from origin increasing)
graph b: distance from home vs time (a line increasing, then flat, then increasing)
graph c: distance from home vs time (a triangle - shaped graph, increasing then decreasing)
graph d: distance from home vs time (a graph increasing, flat, then decreasing)

1. the distance - time graph shows an athlete’s 100 metre race.

(graph: distance from start (metres) on y - axis, time (seconds) on x - axis, a straight line from (0,0) to (16,100) approximately)
a. how long did it take the athlete to run 100 metres?
athlete run after 5 seconds? (incomplete sentence)

Explanation:

Problem 1: Matching Sentences to Graphs

1. "Leave home and travel at a constant speed."

• Explanation: A constant speed on a distance - time graph is represented by a straight line with a positive slope (since distance from home is increasing with time). Graph A has a straight line from the origin (starting at home, distance 0) with a constant slope, so it represents constant speed away from home.
• Answer: A

2. "Leave home, travel at a constant speed, stop for a short time and then return home."

• Explanation: First, there is an increase in distance (constant speed), then a horizontal line (stop, distance doesn't change with time), then a decrease in distance back to 0 (returning home). Graph D has an increase, a horizontal segment (stop), and then a decrease back to the origin.
• Answer: D

3. "Leave home, travel to destination and immediately return."

• Explanation: The distance increases to a maximum (reaching destination) and then immediately decreases back to 0 (returning home) with no stop in between. Graph C has a triangular shape, increasing to a peak and then decreasing back to 0, representing going and immediately coming back.
• Answer: C

4. "Leave home, travel at a constant speed, stop for some time and then continue journey away from home."

• Explanation: First, distance increases (constant speed), then a horizontal line (stop), then another increase in distance (continuing journey away from home). Graph B has an increase, a horizontal segment (stop), and then another increase.
• Answer: B

Problem 2a: Time to Run 100 Metres

Step 1: Analyze the Graph

The graph is a distance - time graph for an athlete's 100 - metre race. The y - axis is distance from start (in metres) and the x - axis is time (in seconds). We need to find the value of x (time) when y (distance) is 100 metres.

Step 2: Find the Time at 100 Metres

Looking at the graph, when the distance (y - value) is 100 metres, we look at the corresponding x - value (time). From the grid, we can see that when distance = 100 metres, the time is 16 seconds (by following the line to the x - axis or looking at the grid intersections).

Answer:

It took the athlete 16 seconds to run 100 metres.