Can Magnitude Of Acceleration Be Negative: 3 Important Facts


When velocity varies over time, it causes acceleration. As a result, it is, therefore, a vector quantity with direction and magnitude. You may come across the term “negative acceleration.” So the question is, can magnitude of acceleration be negative? So, in this article, let’s have a look at this question.

Magnitude, magnitude is nothing more than a vector length that its unit can represent. So we can say that magnitude is the length of a vector directed towards the direction of the vector. Due to the lack of direction, the magnitude of every physical quantity that is a vector is always positive. 

Characteristics of vectors also imply acceleration, as it is also a vector. As a result, the magnitude of the acceleration is likewise a length of the acceleration vector, and the direction of acceleration is towards the acceleration vector. Thus we can conclude that being a value magnitude has no direction.

Now, the question is whether the positive or negative sign in acceleration refers to magnitude or direction.

A positive or negative sign can be used to indicate direction. There are two indicators on the signs:

1) If acceleration is positive, either the speed in the particular direction increases with time, or we have assigned it a positive direction in that frame of reference.

2) Similarly, if acceleration is negative, either the speed in the particular direction decreases with time rather than increasing, or we have assigned it a negative direction in that frame of reference.

As a result, the magnitude of acceleration or any vector can never be negative. It is always positive, although it can also be zero in some cases. Let’s look at a few cases of finding the magnitude of acceleration to check can magnitude of acceleration be negative or not.

The magnitude of acceleration from the definition of acceleration:

As per the definition of acceleration magnitude of the acceleration is given by:

The vertical lines represent the vector’s absolute value, meaning that the value is always positive (or, in some cases, zero).

If an object’s final velocity vf is less than its initial velocity vi, it indicates that the thing is slowing down. That does not imply that the magnitude is negative. Consider a car that is traveling in one direction and then applies the brakes. As a result, the car will experience negative acceleration, which means its final velocity will be lower than its initial velocity even though the magnitude of acceleration will continue to be positive. 

Similarly, assume a car is traveling in the right direction at first. After that, begin going to the left. As a result, acceleration will be negative in this situation. Because we usually associate the right side with positive and the left with negative.The negative sign, on the other hand, does not indicate magnitude but rather the opposite direction.

The magnitude of acceleration in the case of Newton’s Second Law:

With Newton’s second law in mind, acceleration can be calculated as follows:

Can Magnitude Of Acceleration Be Negative

Consider a ball that is falling toward the ground due to the earth’s gravitational pull. The ball accelerates in the same direction as the force that is applied to it. Both gravitational force and gravitational acceleration are negative since they are in a downward direction. On the other hand, the magnitude of the acceleration is not negative and remains constant at 9.8 m/s2.

The magnitude of acceleration from vector components of acceleration:

Assume a1 and a2 are two components of an acceleration vector (It can be two or more, but here we consider two). 

Then acceleration vector has the following magnitude:

We take the square root of the sum of the squared magnitudes of the acceleration components in the magnitude formula. The acceleration magnitude has become positive due to the squared summation.

Solved problem on Finding Acceleration:

Problem 1: 

A guy begins his motion in a straight line at a velocity of 50 m/s and his velocity changes at a constant rate. What would be his acceleration if he stopped after 100 seconds?

Solution: Here’s what we’re given:

vi = 50 m/s initial velocity

At time t = 100 s, a person comes to a complete stop.

vf = 0 m/s final velocity

Thus, acceleration:

Let’s put the values we are given.

The presence of a negative sign indicates that the velocity is decreasing. As a result, the magnitude of the acceleration is:

Which is positive.

Problem 2:

0.98 N force is holding an apple of 0.1 kg. Due to gravity, the apple falls from the tree. Then what would be the acceleration of the apple?

Solution: The following is the information we’ve been given:

Force on apple F = 0.98 N

Mass of apple m = 0.1 kg

Then the acceleration of the apple g =?

[ Gravity is the cause of acceleration here. As a result, “g” is used to represent it instead of “a.”]

=9.8 m/s2

This is the gravitational acceleration’s value. Everywhere on the earth, this value remains constant.

Problem 3:

A car is going in the east direction with a speed of 10 m/s. Then after 10 s, it takes turns in the west direction, but its speed remains constant. Is the car said to be accelerated or not? If yes, what is the magnitude of acceleration?

Solution: Velocity of car in East direction ve = 10 m/s

Similarly velocity of car in west direction vw = 10 m/s

Time interval t = 10 s

The magnitude of velocity is the same in both cases, which is 10 m/s. However, the directions are not the same. As a result of the change in direction, acceleration is produced. The magnitude of the acceleration is as follows:

Alpa P. Rajai

I am Alpa Rajai, Completed my Masters in science with specialization in Physics. I am very enthusiastic about Writing about my understanding towards Advanced science. I assure that my words and methods will help readers to understand their doubts and clear what they are looking for. Apart from Physics, I am a trained Kathak Dancer and also I write my feeling in the form of poetry sometimes. I keep on updating myself in Physics and whatever I understand I simplify the same and keep it straight to the point so that it deliver clearly to the readers. You can also reach me at : https://www.linkedin.com/in/alpa-rajai-858077202/

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