Question

What is the average acceleration of the particle between 0 seconds and 4 seconds? a. 0 meters/second2 b. 0.04 meters/second2 c. 0.06 meters/second2 d. 0.25 meters/second2 e. 0.928 meters/second2

Answer 1

The average acceleration of the particle between 0 seconds and 4 seconds is 0 meters/second².

So.the correct option is B.

Step-by-step explanation:

The average acceleration is determined by dividing the change in velocity by the time interval. In this case since the particles velocity remains constant over the given time interval (0 to 4 seconds) there is no change in velocity and therefore the average acceleration is zero.

This is because acceleration is the rate of change of velocity and when there is no change in velocity the acceleration is zero. So the correct answer is 0 meters/second². Acceleration is a vector quantity meaning it has both magnitude and direction.

In cases where the velocity remains constant as in uniform motion the acceleration is zero. Understanding the relationship between velocity and acceleration is fundamental in physics and kinematics. It helps describe the motion of objects and is a key concept in classical mechanics.

So.the correct option is B.

Answer 2

The average acceleration of the particle between 0 seconds and 4 seconds is
`\(0.05\)` meters per second squared. However, this value is not one of the options provided. The closest option to
`\(0.05\)` meters per second squared is:

c.
`\(0.06\)` meters/second²

Given the coordinates (2, 2) and (4, 0.2), we can calculate the average acceleration between 2 seconds and 4 seconds. The change in velocity
`(\( \Delta v \))` is the difference between the final velocity and the initial velocity. The change in time
`(\( \Delta t \))` is the difference between the final time and the initial time.

The formula for average acceleration is:

`\[ a_{\text{avg}} = (\Delta v)/(\Delta t) \]`

Where:

-
`\( v_f \)` = final velocity = 0.2 m/s (at
`\( t = 4 \)` seconds)

-
`\( v_i \)` = initial velocity = 2 m/s (at
`\( t = 2 \)` seconds)

-
`\( t_f \)` = final time = 4 seconds

-
`\( t_i \)` = initial time = 2 seconds

Let's plug these values into the formula and calculate the average acceleration.

The average acceleration of the particle between 2 seconds and 4 seconds is \(-0.9\) meters per second squared. This indicates the particle is decelerating, as the velocity is decreasing over time.

However, the question asked for the average acceleration between 0 seconds and 4 seconds, so we would need the velocity at 0 seconds to calculate this. Since the velocity at 0 seconds was not explicitly given, we'll need to infer it based on the graph. If we assume that the graph starts from the origin and the velocity at 0 seconds is 0 m/s, then the initial velocity
`\( v_i \)` at
`\( t = 0 \)` seconds is 0 m/s, and the final velocity
`\( v_f \)` at
`\( t = 4 \)` seconds is 0.2 m/s.

Let's calculate the average acceleration over the entire interval from 0 to 4 seconds with these assumptions.

The average acceleration of the particle between 0 seconds and 4 seconds is
`\(0.05\)` meters per second squared. However, this value is not one of the options provided. The closest option to
`\(0.05\)` meters per second squared is:

c.
`\(0.06\)` meters/second²

It's worth noting that the value calculated is based on an assumption about the velocity at 0 seconds and the exact velocity at 4 seconds. If these assumptions were incorrect, the actual average acceleration might be different. If you need further clarification or assistance, please let me know!