Question 1: Relative Motion Between Two Cars

Given:

• One car is travelling at 10 m/s in one direction.
• The other car is travelling at 5 m/s in the opposite direction.

To find the relative velocity, we simply add the speeds of the two cars, as they are moving towards each other (opposite directions):

$\text{Relative velocity} = 10 \, \text{m/s} + 5 \, \text{m/s} = 15 \, \text{m/s}$

So, the correct answer is:

A. 15 m/s

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Question 2: Acceleration of a Person on a Roundabout

In this case:

• The person on the roundabout is moving at a constant speed (i.e., the speed doesn’t change).
• However, their direction of motion is changing as they spin around the center of the roundabout.

Since acceleration is a vector quantity, it depends on both the magnitude (speed) and direction of motion. Even though the person’s speed is constant, the fact that they are changing direction means that their velocity is constantly changing, which results in an acceleration.

This type of acceleration is called centripetal acceleration, and it is directed towards the center of the roundabout.

So, the correct description is:

B. They are accelerating because they are changing direction as they spin

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Would you like further details or have any questions about this?

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Related Questions:

1. What is the formula for calculating relative velocity when two objects move in opposite directions?
2. How does centripetal acceleration depend on speed and radius?
3. What would happen to the relative velocity if the cars were moving in the same direction instead?
4. How can we determine the direction of acceleration for an object moving in a circular path?
5. What other types of acceleration exist besides centripetal acceleration?

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Tip: Remember that when two objects move in opposite directions, you add their velocities to find the relative velocity.