How To Find Acceleration With Coefficient Of Friction: Exhaustive Approaches And Facts

How to find acceleration with coefficient of friction is another important and conventional topic that needs to be dealt with. It is a factor that enhances acceleration in a particular way possible.

When a body is in motion, it will continue to in the same until a force acts upon it that changes the object’s dimensions. So this process will go on unless a speed is increased or decreased.

Once the object changes speed, it will either be accelerated (positive) or decelerated (negative), usually in the opposite direction of the action of motion. The change in speed is also known as velocity in physics terms.

The change in speed happens at a different time, and hence this will influence the acceleration of the body in motion either positively or negatively. A sudden jerk in the system gives the acceleration a change also.

When a body is under motion, there are several factors that influence and one of those is acceleration, which will be affected by the term called friction. Slowly we will be dealing with finding acceleration with coefficient of friction.

We can keep talking about acceleration in so many ways, but when another factor affects the acceleration, we need to focus on that. Friction is fundamentally the factor present between the body and the active surface.

Understanding of friction and coefficient of fiction 

Before we dive into this in detail, first knowledge about friction and coefficient of friction is required. Friction is basically the force that resists the motion while walking, running, and so many. 

There is a small factor that is present in between the object and the surface and that is called as the friction. That particular force is called as the frictional force. This force helps in any random body in action to be able to move.

When the surface is rough, the friction is more, and when the surface is smooth, the friction is more minor. So when friction increases, acceleration decreases, and when friction decreases, acceleration decrease. This is the basic understanding in familiar terms as well.

Now let us look into what exactly coefficient of friction means. This coefficient of friction is the one that is a dimensionless factor which is the ratio between normal force and frictional force of a body in motion.

So we all know that several different aspects contribute to the movement of a body. It will be accelerated by one way or the other. Firstly it is the change of speed called velocity that helps in the mobility of the body.

In certain cases it seems to be essential too. It will be external force or any other force and the net force as a whole. The factor called friction has major contributions to the movement of any object or a body. The coefficient of friction will decide how much force will be required for such a motion of the body.

Since it is the measure of ratio, it will have zero dimensions, and will the value will vary between a minimum of 0 to 0.5 of maximum. There can also be the coefficient of friction that can go greater than one also.

How to find acceleration with coefficient of friction

Knowledge about the formula to find the acceleration is required. As per Newton’s Second Law, the acceleration is proportional to the force and indirectly proportional to the mass of the object.

Hence, we derive it as a = F / m. this is the formula for basic acceleration without any attributes. When friction is acting upon the body and motion of it, the type of surface is also equally important.

So the formula is changed according to the coefficient of friction, a = (fn-μ)/m. μ is known as the coefficient of friction, and this will indicate the amount of force required to move the body further in motion.

Let us see how this is using a better example. Rightward friction of 10N is applied on a 7kg weighing body. It is allowed to accelerate on a rough surface. The force of friction has a value of 0.3N. Now calculate the acceleration of the object.

a = (20 – 0.3) / 7

a = 19.7/7

a = 2.81 ms-2

So this is how to find acceleration with coefficient of friction. But where the use of coefficient of friction is is the question. We will deal with that too. In the question, the friction force constant is directly given.

The frictional force and the force of normal will not be given explicitly but using friction coefficient the values can be drawn. From the data given, we must calculate the coefficient of friction to apply it to the formula and find the acceleration.

Problem on how to find acceleration with coefficient of friction

how to find acceleration with coefficient of friction


An 1100kg of the car with a coefficient of friction having value μ= 0.95 concerning the tires. Now determine the acceleration. It moves with a force of 880N.


We need to understand this problem using a free-body diagram. Now let us dive into the motion of the car and the kind of forces acting upon it. Since the car is in motion, it will experience as many forces as possible.

We know that by default, a normal force acts on the body; now, since it is in motion, a frictional force acts as well.

The value given for the coefficient of friction is μ= 0.95. Here we need to find the frictional and normal forces since the coefficient of friction value is already given.

We need to note that normal force is equal to the gravitational force. It is known that the force of gravity is 9.8ms-1. And now, that value multiplied by the mass gives the normal force. Fn= 1100×9.8 = 10780. 

Force of friction is the coefficient of friction times the normal force. Hence ff =10241. Now that force of friction is found next step is to find the acceleration. The frictional force is also considered as the net force.

a= f/m

a= 10241/1100

a= 9.31ms-2

Frequently Asked Questions

How do you find velocity with friction?

Since acceleration could be found with friction, velocity could also be found since it is nothing but speed change.

First, we need to know the initial velocity and the force of gravity. So the velocity with friction is found by the formula, initial velocity minus the coefficient of friction times the force of gravity and the time given. v(t) = v0 – μ g t.

How to find the coefficient of friction?

The coefficient of friction is the factor that is present between the body under motion and the surface with which it is in motion.

The formula for coefficient of friction is, μ = (frictional force) / (force of normal). Another point to be noted is that the frictional force is sometimes equal to the net force acting on the body, which makes it easier to calculate the acceleration. The normal force is calculated by multiplying the force of gravity and the mass of the body.

What are the different types of friction?

Static and kinetic friction is the two different types that come under one topic of friction.

Static friction is known as friction when a body is not under any motion. It is evident from the word static itself that nothing is in motion. In such cases, the friction found is called static friction. When a body moves away from its equilibrium it is also due to friction and that kind is called as kinetic friction.  The static and kinetic friction differs according to the cases, and conditions are given.

Why static friction is called so?

Static friction is called so because it is the force that opposes the body that is not under motion.

When a body does not move and stays in an equilibrium position, the kind of friction acting on the body is called static friction. This friction always acts in the opposite direction to force acting along with the body’s motion even when not in action.

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