Question Video: Using a Displacement–Time Graph to Describe the Speeds and Velocities of Two Objects | Nagwa Question Video: Using a Displacement–Time Graph to Describe the Speeds and Velocities of Two Objects | Nagwa

# Question Video: Using a Displacement–Time Graph to Describe the Speeds and Velocities of Two Objects Physics • First Year of Secondary School

## Join Nagwa Classes

The change in displacement of two objects with time is shown in the graph. The lines plotted on the graph are parallel. Which of these statements about the speeds and velocities of the two objects is correct? [A] Their speeds are the same, but their velocities are different. [B] Their velocities are the same, but their speeds are different. [C] Both their speeds and velocities are different. [D] Both their speeds and velocities are the same.

02:48

### Video Transcript

The change in displacement of two objects with time is shown in the graph. The lines plotted on the graph are parallel. Which of these statements about the speeds and velocities of the two objects is correct? (A) Their speeds are the same, but their velocities are different. (B) Their velocities are the same, but their speeds are different. (C) Both their speeds and velocities are different. (D) Both their speeds and velocities are the same.

This question has given us a displacement–time graph; that’s a graph that plots displacement on the vertical axis against time on the horizontal axis. We are being asked about the speeds and velocities of the two objects whose motion is shown on this graph.

Let’s recall that displacement and velocity are vector quantities, which means that they have both a magnitude and a direction. Meanwhile, speed is a scalar quantity, so it has just a magnitude and no associated direction. The speed of an object is equal to the magnitude of that object’s velocity. And the velocity of an object is equal to the rate of change of displacement with time.

Looking at the graph, we can see that the two objects have different initial and final displacements. The object represented by the blue line begins at some positive initial displacement and ends up at a displacement of zero. The object represented by the red line begins at a smaller positive displacement and ends up at a negative displacement value.

Since the displacement of both objects is decreasing as time goes on, then both objects must be traveling in the negative direction; that is, their velocities must both be negative. So, the direction of the velocity of each object is the same. But what about the magnitudes? We’ve said that the velocity of an object is equal to the rate at which its displacement changes with time.

Since a displacement–time graph has displacement plotted against time, then this means that the velocity of an object is given by the slope of the corresponding line on a displacement–time graph. We’re told that both these two lines on the graph are parallel, which means that they have the same slope. Therefore, not only do the two objects move in the same direction, but the magnitude of their velocity in this direction is also equal. We have found then that both objects have the same value of velocity.

Since we know that an object’s speed is equal to the magnitude of its velocity, and we’ve seen that both objects here have the same magnitude velocity, then we know that these two objects must also have equal speeds. Since the objects here have the same velocity and the same speed as each other, then we can identify the correct answer as option (D): both their speeds and velocities are the same.

## Join Nagwa Classes

Attend live sessions on Nagwa Classes to boost your learning with guidance and advice from an expert teacher!

• Interactive Sessions
• Chat & Messaging
• Realistic Exam Questions