Distance-Time Graphs

Match the following concepts with their representations on a distance-time graph.

• Curvature of the graph

• Time

• Slope of the graph

• Acceleration

• Horizontal axis

• Distance

• Vertical axis

• Speed

Answer explanation

The slope of a distance-time graph indicates how much distance is covered over a specific time period. This ratio represents speed, making it the correct choice. Thus, the slope shows how fast an object is moving.

Match the following descriptions with the type of line you would see on a distance-time graph.

• A line that rises sharply

• Steep line

• A line that maintains a constant slope

• Flat line

• A line that remains horizontal

• Curved line

• A line that changes direction continuously

• Straight line

Answer explanation

A boat traveling at a constant speed will cover equal distances in equal time intervals, resulting in a straight line on a distance-time graph. This indicates a consistent rate of travel.

Tags

NGSS.MS-PS3-1

Match the following scenarios with their speeds.

• Distance: 10m, Time: 2s

• 2.0 m/s

• Distance: 20m, Time: 2s

• 10.0 m/s

• Distance: 4m, Time: 2s

• 15.0 m/s

• Distance: 30m, Time: 2s

• 5.0 m/s

Answer explanation

To find the speed of the boat, calculate the change in distance over the change in time. The distance from (2, 10) to (6, 30) is 20 meters (30-10) over 4 seconds (6-2), giving a speed of 5.0 m/s.

Tags

NGSS.MS-PS3-1

Imagine Aarav and Chloe are watching a distance-time graph. A flat line (slope = 0) on this graph means (a)   . Can you guess what it indicates?

• Constant speed

• Stopping or no motion

• Increasing speed

• Decreasing speed

Answer explanation

A flat line (slope = 0) on a distance-time graph indicates that the object is not changing its position over time, meaning it is stopped or in no motion. Therefore, the correct answer is 'Stopping or no motion'.

Match the following symbols with their meanings in a graph.

• Total Distance

• The starting point

• Starting Point

• The total distance covered

• Average Speed

• The average speed

• Δ

• The change in distance or time

Answer explanation

In graphs, "Δ" (delta) signifies the change in a variable, such as distance or time. It indicates how much a quantity has increased or decreased, making "The change in distance or time" the correct choice.

Imagine Neha and Thomas racing on a track. A steeper slope on their distance-time graph means a (a)   speed. Who's winning?

• True

• False

Answer explanation

True. A steeper slope on a distance-time graph indicates that distance is changing more rapidly over time, which means a faster speed.

Tags

NGSS.MS-PS3-1

Chloe and Aiden are racing toy cars on a track. To find out who is faster, they use the slope formula from their distance-time graph: (a)  

• 𝑦2−𝑦1𝑥2−𝑥1

• 𝑥2−𝑥1𝑦2−𝑦1

• 𝑦2𝑦1

• 𝑥2+𝑥1

Answer explanation

The slope formula, 𝑦2−𝑦1/𝑥2−𝑥1, calculates the rate of change, which in a distance-time graph represents speed. Here, 𝑦 represents distance and 𝑥 represents time, making this the correct choice.

Tags

NGSS.MS-PS3-1

During a thrilling boat race, Aarav's boat zooms (a)   in just 10 seconds. Can you guess the distance?

• 10 m

• 30 m

• 50 m

• 100 m

Answer explanation

The boat travels at a speed of 5 m/s. In 10 seconds, it covers a distance of 5 m/s * 10 s = 50 m. Therefore, the correct answer is 50 m.

Imagine Henry and Mira are racing their toy cars at the same speed. On a distance-time graph, their lines will be (a)   .

• True

• False

Answer explanation

True. When two cars travel at the same speed, they cover equal distances in equal time intervals, resulting in parallel lines on a distance-time graph.

Tags

NGSS.MS-PS3-1

Imagine Kiara and Lucas are racing on a distance-time graph. A straight line indicates (a)   . Who's winning?

• Uniform motion (constant speed)

• Accelerating motion

• Decelerating motion

• No motion

Answer explanation

A straight line on a distance-time graph indicates uniform motion, meaning the object is moving at a constant speed. The slope of the line remains the same, showing that distance increases steadily over time.

Tags

NGSS.MS-PS3-1