Let's analyze the two instances described in your question:

f.) The body initially moves to the left at 20 m/s, then ends up moving to the right at 20 m/s with an acceleration of $4.0 \, \text{m/s}^2$ to the right.

To determine deceleration, we need to understand that deceleration refers to a reduction in speed. However, in physics, "deceleration" is not always straightforward—it depends on the direction of motion and the direction of acceleration.

1. Initial Motion:

   • The body moves to the left at 20 m/s. This means its velocity is negative with respect to a rightward direction (assuming left is negative).

2. Final Motion:

   • The body ends up moving to the right at 20 m/s. This means its velocity is positive (rightward).

3. Acceleration:

   • The acceleration is given as $4.0 \, \text{m/s}^2$ to the right, which means it acts to change the velocity to the right.

Is this deceleration?

• The object initially moving to the left (negative velocity) is being accelerated in the right direction (positive acceleration), which results in a reduction of its leftward speed (deceleration in leftward direction).
• Afterward, the object moves to the right, where the acceleration increases the speed in the rightward direction.

Thus, during the first part of the motion, while the object is still moving left but accelerating right, the body is decelerating as it slows down its leftward motion before reversing direction.

g.) In which of the above instances has the body decelerated?

The body decelerates in instance f when it is slowing down its leftward motion due to the rightward acceleration before changing direction.

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Would you like more details or have any questions?

Here are some related questions to expand your understanding:

1. What is the difference between deceleration and negative acceleration?
2. Can an object accelerate without changing its speed?
3. How do we determine the sign of acceleration in different directions?
4. How does uniform acceleration affect velocity over time?
5. How does the concept of deceleration apply when the object reverses direction?

Tip: Deceleration always refers to a reduction in speed, but its interpretation depends on both the velocity and the direction of acceleration.