Speed-Time Graphs and Motion

What does it mean if the speed of an object remains constant over time?

• The object is speeding up

• The object is slowing down

• The object is in uniform motion

• The object has stopped

Answer explanation

If the speed of an object remains constant over time, it indicates that the object is moving at a steady rate without acceleration or deceleration, which is defined as uniform motion.

Which of the following represents the boat's speed in a uniform motion?

• The speed decreases over time

• The speed is constant at 5.0 m/s

• The speed increases every second

• The speed is zero

Answer explanation

In uniform motion, the speed remains constant. The correct choice, 'The speed is constant at 5.0 m/s', indicates that the boat maintains a steady speed without acceleration or deceleration.

On a speed-time graph, a positive slope indicates that the object is (a)  

• The object is slowing down
• The object is speeding up
• The object is moving at a constant
• The object has stopped

Answer explanation

A positive slope on a speed-time graph indicates that the speed of the object is increasing over time, meaning the object is speeding up.

Tags

NGSS.MS-PS3-1

If the horizontal line on a speed-time graph is at the bottom (0 m/s), what does it indicate?

• The object is speeding up

• The object is moving at a constant speed

• The object has stopped

• The object is slowing down

Answer explanation

A horizontal line at 0 m/s on a speed-time graph indicates that the object's speed is zero, meaning it has stopped. Therefore, the correct choice is that the object has stopped.

Tags

NGSS.MS-PS3-1

What is the slope of a horizontal line on a speed-time graph?

• Positive

• Negative

• Zero

• Undefined

Answer explanation

The slope of a horizontal line indicates no change in speed over time. Therefore, the slope is zero, meaning the speed remains constant.

What does the area under the line of a speed-time graph represent?

• Time

• Distance traveled

• Speed

• Acceleration

Answer explanation

The area under the line in a speed-time graph represents the total distance traveled. This is because distance is calculated as speed multiplied by time, which is visually represented by the area.

Tags

NGSS.MS-PS3-1

Calculate the area under the graph between 0 and 10 seconds if the speed is constant at 5.0 m/s.

• 25 m

• 50 m

• 10 m

• 5 m

Answer explanation

To find the area under the graph (distance), use the formula: Area = speed × time. Here, speed = 5.0 m/s and time = 10 s. Thus, Area = 5.0 m/s × 10 s = 50 m. Therefore, the correct answer is 50 m.

Tags

NGSS.MS-PS3-1

Match the following scenarios with the correct formula to calculate the area under the speed-time graph.

• Rectangle with length and width

• Area = base × height

• Constant speed over time

• Area = speed × time

• Rectangle with base and height

• Area = ½ × base × height

• Triangle with base and height

• Area = length × width

Answer explanation

The area under a speed-time graph represents the distance traveled. When the object is speeding up, the graph forms a triangle. The correct formula for the area of a triangle is Area = ½ × base × height.

If an object is slowing down, what is the shape of the area under the speed-time graph?

• A square

• A triangle

• A circle

• A rectangle

Answer explanation

When an object is slowing down, its speed decreases over time, creating a triangular shape on a speed-time graph. The area under the graph represents distance, and a triangle accurately reflects this decreasing speed.

Match the following scenarios with their total distances traveled.

• Speeds up for 7.5 m, travels at constant speed for 20 m, and slows down for 5 m

• 25 m

• Speeds up for 20 m, travels at constant speed for 20 m, and slows down for 10 m

• 33 m

• Speeds up for 3 m, travels at constant speed for 5 m, and slows down for 2 m

• 10 m

• Speeds up for 5 m, travels at constant speed for 15 m, and slows down for 5 m

• 50 m

Answer explanation

The total distance is the sum of all segments: 7.5 m (speeding up) + 20 m (constant speed) + 5.0 m (slowing down) = 32.5 m. Rounding to the nearest whole number gives 33 m, which is the correct answer.