Acceleration, and displacement

In summary: However, if we use Δx/Δt2, we get 10 m/s^2. This is the correct answer because the acceleration is proportional to the change in velocity.
  • #1
jaja1990
27
0
I think we can't have a negative displacement. Is that right?

Acceleration: the change in displacement / change in time squared
Since displacement can't be negative, and time can't be negative, acceleration also can't be negative.
But I know (it's in the books) that when we have decreasing acceleration, it's negative. How is that?
 
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  • #2
jaja1990 said:
I think we can't have a negative displacement. Is that right?
Why do you think this? Realize that whether a vector is negative or not just depends on the sign convention used when specifying its components.
Acceleration: the change in displacement / change in time squared
Better to think of acceleration as Δv/Δt.
Since displacement can't be negative, and time can't be negative, acceleration also can't be negative.
Again, the sign of a vector is rather arbitrary.
But I know (it's in the books) that when we have decreasing acceleration, it's negative. How is that?
Acceleration is a vector. A negative acceleration just means that the acceleration vector points in the negative direction. For example, if you take up as positive, the acceleration of a falling body will be negative.
 
  • #3
Doc Al said:
Why do you think this? Realize that whether a vector is negative or not just depends on the sign convention used when specifying its components.

Better to think of acceleration as Δv/Δt.

Again, the sign of a vector is rather arbitrary.

Acceleration is a vector. A negative acceleration just means that the acceleration vector points in the negative direction. For example, if you take up as positive, the acceleration of a falling body will be negative.
I understand now, it's the direction that is negative, not the magnitude.

Why is it better to think of acceleration as Δv/Δt?
I guess it just a matter of which is more intuitive/elegant, but maybe there is another reason; is there?
 
  • #4
Acceleration is the derivative of the velocity so it's dv/dt.

The sign of the acceleration can have different criteria, I think an acceleration is negative if the scalar product (dv/dt)•v < 0 and positive if (dv/dt)•v > 0. If the scalar product it's zero then the acceleration is perpendicular to the motion. This is the case in circular motion, for example.
 
  • #5
jaja1990 said:
Why is it better to think of acceleration as Δv/Δt?
I guess it just a matter of which is more intuitive/elegant, but maybe there is another reason; is there?
Well, Δv/Δt is the definition of acceleration (at least average acceleration).

Blindly using Δx/(Δt)2 can lead to silly results. Imagine something moving at a constant velocity of 10 m/s for 1 second. Δx = 10, Δt = 1. Obviously the acceleration is zero here, so that formula fails.
 

1. What is acceleration?

Acceleration is the rate of change of velocity over time. It measures how quickly an object's speed is changing, either by increasing or decreasing.

2. How is acceleration calculated?

Acceleration can be calculated by dividing the change in an object's velocity by the time it took for that change to occur. The formula for acceleration is: a = (v2 - v1) / t, where a is acceleration, v2 is the final velocity, v1 is the initial velocity, and t is the time interval.

3. What is the difference between positive and negative acceleration?

Positive acceleration occurs when an object's speed is increasing, while negative acceleration (also known as deceleration) occurs when an object's speed is decreasing. Acceleration can also be zero if an object's velocity remains constant.

4. What is displacement?

Displacement is the shortest distance between an object's initial position and its final position, taking into account the direction of motion. It is a vector quantity, meaning it has both magnitude (distance) and direction.

5. How is displacement different from distance?

Distance is a scalar quantity that measures the total path length traveled by an object, regardless of direction. Displacement, on the other hand, considers only the shortest distance between the initial and final positions, taking direction into account.

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