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The average acceleration a over a time interval is defined as
- a)average velocity divided by the time interval
- b)the change of velocity divided by the time interval
- c)average speed divided by the time interval
- d)average displacement divided by the time interval
Correct answer is option 'B'. Can you explain this answer?
Verified Answer
The average acceleration a over a time interval is defined asa)average...
Explanation:
Acceleration is the rate of change of velocity with time.It is a vector quantity.
Average acceleration is the change in velocity per unit time over an interval of time.
Let initial velocity at time interval t1 is v1 and final velocity at time interval t2 is v2 Then
Most Upvoted Answer
The average acceleration a over a time interval is defined asa)average...
Definition of average acceleration:
Average acceleration is defined as the change in velocity divided by the time interval in which the change occurs. It is a measure of how quickly an object's velocity changes over time.
Explanation:
Acceleration is a vector quantity that represents the rate at which an object's velocity changes. It can be positive or negative, depending on whether the object is speeding up or slowing down. The average acceleration is determined by calculating the change in velocity and dividing it by the time interval over which the change occurs.
Change in velocity:
The change in velocity is determined by subtracting the initial velocity from the final velocity. If an object starts with an initial velocity of v1 and ends with a final velocity of v2, the change in velocity is given by v2 - v1.
Time interval:
The time interval is the duration over which the change in velocity occurs. It is usually denoted by Δt and represents the difference between the final and initial times. If an object starts at time t1 and ends at time t2, the time interval is given by t2 - t1.
Calculating average acceleration:
To calculate the average acceleration, we divide the change in velocity by the time interval. Mathematically, it can be expressed as:
Average acceleration (a) = (v2 - v1) / (t2 - t1)
This equation shows that the average acceleration is equal to the change in velocity divided by the time interval. Therefore, the correct answer is option 'B' - the change of velocity divided by the time interval.
Example:
Let's consider an example to illustrate this concept. Suppose a car initially travels at a velocity of 20 m/s and after 5 seconds, its velocity increases to 40 m/s. The change in velocity is 40 m/s - 20 m/s = 20 m/s. The time interval is 5 seconds. Therefore, the average acceleration would be:
Average acceleration = (20 m/s)/(5 s) = 4 m/s²
This means that the car's velocity is increasing at a rate of 4 meters per second squared.
Average acceleration is defined as the change in velocity divided by the time interval in which the change occurs. It is a measure of how quickly an object's velocity changes over time.
Explanation:
Acceleration is a vector quantity that represents the rate at which an object's velocity changes. It can be positive or negative, depending on whether the object is speeding up or slowing down. The average acceleration is determined by calculating the change in velocity and dividing it by the time interval over which the change occurs.
Change in velocity:
The change in velocity is determined by subtracting the initial velocity from the final velocity. If an object starts with an initial velocity of v1 and ends with a final velocity of v2, the change in velocity is given by v2 - v1.
Time interval:
The time interval is the duration over which the change in velocity occurs. It is usually denoted by Δt and represents the difference between the final and initial times. If an object starts at time t1 and ends at time t2, the time interval is given by t2 - t1.
Calculating average acceleration:
To calculate the average acceleration, we divide the change in velocity by the time interval. Mathematically, it can be expressed as:
Average acceleration (a) = (v2 - v1) / (t2 - t1)
This equation shows that the average acceleration is equal to the change in velocity divided by the time interval. Therefore, the correct answer is option 'B' - the change of velocity divided by the time interval.
Example:
Let's consider an example to illustrate this concept. Suppose a car initially travels at a velocity of 20 m/s and after 5 seconds, its velocity increases to 40 m/s. The change in velocity is 40 m/s - 20 m/s = 20 m/s. The time interval is 5 seconds. Therefore, the average acceleration would be:
Average acceleration = (20 m/s)/(5 s) = 4 m/s²
This means that the car's velocity is increasing at a rate of 4 meters per second squared.
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Community Answer
The average acceleration a over a time interval is defined asa)average...
The correct answer is indeed option B: "the change of velocity divided by the time interval."
Here's why:
Average Acceleration (a) is defined as the rate of change of velocity (Δv) over a given time interval (Δt). Mathematically, it's represented as:
a = Δv / Δt
or
a = (v₂ - v₁) / (t₂ - t₁)
where:
- v₁ is the initial velocity
- v₂ is the final velocity
- t₁ is the initial time
- t₂ is the final time
In simpler terms, acceleration measures how quickly an object changes its velocity. If an object's velocity increases or decreases over time, it's accelerating.
Why option B is correct:
- "The change of velocity" (Δv) represents the difference between the final and initial velocities.
- "Divided by the time interval" (Δt) represents the time over which this change occurs.
Why other options are incorrect:
- Option A: Average velocity is not directly related to acceleration. Average velocity would be the total displacement divided by the time interval.
- Option C: Average speed is a scalar quantity, whereas acceleration is a vector quantity. Average speed doesn't account for direction changes.
- Option D: Average displacement divided by time interval would give average velocity, not acceleration.
I hope this explanation helps clarify the concept!
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