Free Tutorial in Basic Physics - Understanding Acceleration


There are many things to learn in basic Physics. Acceleration is one of them. When the velocity of a body increases then we say that it has acceleration. Understanding acceleration helps in understanding the various things about a moving body. This article is an effort to explain the concept of acceleration in simple terms.

Introduction

In some earlier basic Physics articles we learnt the basic concepts about many things like Density, Electric voltage, and Electric current. Now in this article we will learn about the entity known as 'Acceleration'.

When a body moves from one place to another then we say that it has a speed with which it travelled from starting point to the endpoint. When we know the direction in which the body is moving then the word speed is replaced with 'velocity' which is an entity with a value as well as a direction. So the value of velocity is actually speed and direction gives it additional information about the exact direction in space where it would be moving. In Physics terminology, speed is a scaler quantity while velocity is a vector quantity. A vector quantity has two components - one is value and the other is direction. Now the question comes whether the body was moving with a fixed velocity or its velocity was changing with time. The next question that arises is that if its velocity was changing then what was the rate of that change and whether it was increasing or decreasing. We will go through all these aspects in this article and will learn about the entity 'Acceleration' which will give an explanation for the change in the velocity of the body.

Displacement and Velocity

Let us first understand these two terms, that is, displacement and velocity.

In Physics we say that when a body is moved from one point to another point then it brings the concept of displacement. The displacement tells us how much distance the body moved from its initial position to its present position and it also tells us in which direction it moved. For example, if a boy walks on a straight road for 100 meters and then comes back 40 meters on the same road and stays at that point then the total distance travelled by him is 100 + 40 = 140 meters. But his displacement from the point of origin is not 140 meters. The reason is that he went in one direction and then came back to a point which is only 60 meters from the point of origin and then we say that his displacement is 60 meters from the original point. To understand it in a different way let us think that first he walked 100 meters in the East direction and then took a U-turn and moved 40 meters in the west direction and his final location is only 60 meters in the East from the point of origin. We have to note that distance is a scaler quantity while displacement is a vector quantity. So we should differentiate between the distance travelled and displacement made. Many students mix up these two entities and commit mistakes in their Physics problem calculations.

  • Example-1: A person goes 200 meters in North direction, then goes 500 meters in East direction, then goes Southwards 300 meters, and then finally goes 500 meters in West direction. Let us find out what is his displacement from the original point.

    Solution-1: These problems are easily solved by drawing the path taken by the person in a graph paper and if we do that we will find that the person has come back near to his initial point and now he is at 100 meters from the original point in the South direction. So his displacement is 100 meters only though the total distance travelled by him is 1500 meters. The student can draw this displacement vector by making a straight line starting at the original point and ending at the final point with an arrow sign at the ending point.

Let us now try to understand the concept of velocity. When a person walks from one point to another in a straight line then he takes some time in it. For the purpose of simplicity let us assume that he is moving with a constant velocity. If his displacement is 'd' and he takes time 't' in travelling through it then his velocity (v) is d/t and it is in the same direction as that of the displacement and its value is d/t.

  • Example-2: Let us consider a simple example of a bird flying in a straight line with a constant velocity of 6 meters/second. It has to reach from one building top to another building top having a separation of 300 meters. Can we find out as how much time it will take for that?
    Solution-2: Using the relationship between velocity, displacement, and time we can do it. So, putting the values in that equation we get 6 = 300/t, which gives us t=50 seconds. For the understanding purpose we had assumed that bird will be moving at a constant velocity and in a straight path but in practice it will be a slightly curved path and not a straight line and velocity would also vary so the exact calculations will require the use of aerodynamic and advanced Physics but for our understanding purposes we have made it too simple and used the basic relationship that is v = d/t.

Acceleration

When a body is moving it has some velocity having some value and direction. If the velocity is constant then we say that it has no acceleration. Sometimes velocity might change which depends upon the external forces and then the body can gain speed or lose it and then we say that it is accelerating or decelerating. Let us take the example of a ball which we push on the ground and it moves ahead but after sometimes it stops. Initially, it moved with a good velocity because we pushed it but slowly it loses its speed because of the frictional forces acting between the ground and the ball which oppose the ball's movement in a forward direction and finally ball comes to the rest. Frictional forces are very important and affect the motions of bodies though we do not perceive them like we perceive the force with which we pushed the ball. The slowing down of the ball is an example of decelerating.

Let us now try to understand acceleration by the movement of a car when a person starts it and drives. The car is started and then the driver pushes on its accelerator lever and the speed of the car starts increasing and then reaches a value at which the driver wants to drive it. Have you ever observed that the speed of the car is increased from zero to 40-50 Km/hour within a few seconds when the driver pushes down on the accelerator lever? During these few seconds, the car is accelerated and moves ahead and attains the desired velocity.

If a body is moving ahead with acceleration and its velocity changes from v1 to v2 in time t then the acceleration (f) is given by f = (v2-v1)/t. The unit of acceleration is metre/second square.

  • Example-3: A rocket is launched upwards and within 1 minute its velocity changes from 500 metres/second to 2 km/second. What is its acceleration?
    Solution-3: Let us take everything in metres and seconds (MKS system). As we know that f = (v2-v1)/t so using this formula we get -
    f = (2000 - 500)/ 60 = 25 metres/second square. In another way we can also say that the velocity of the rocket is increasing by 25 metres/second every second.

Force is required for creating acceleration

If we want to create an acceleration in a body then we will have to apply a continuous force on it to maintain that acceleration. This is a very important point. For example, if we just push a football with our feet then it will move to some distance and then due to the frictional forces acting on it in the opposite direction, it would stop. We had just pushed it with a momentary force with which it could move to some distance. But if we carry it by pushing it continuously with our feet by running along with it then it will continue moving. Another important point in this matter is that the direction of force should be in the direction of the movement. If we apply a force in opposite direction on a moving body then instead of accelerating it will decelerate and finally stop and then start moving in the direction of the force which is in opposite direction.

Let us take a very common example which we all have seen sometime or other. If we throw a ball upwards in the air then what happens? It goes up to some height and then stops and then starts falling down. Why? The answer is simple. We have thrown the ball upwards so with that force it goes up to some height but the gravitational pull of Earth on this ball is applying a force of gravity on it in the opposite direction that is the downward direction. So, the ball will finally stop and then start coming down under the influence of that gravitational force. Please note that the gravitational force is being applied on the ball continuously so it will create an acceleration on it and the velocity of the ball will be increasing every second while coming down. Incidentally, this acceleration is a very important thing in Physics and is known as acceleration due to gravity. Just for information, the value of this acceleration at the surface of Earth is about 9.8 meter/second square.

When a rocket is fired upwards from Earth to go to the Earth orbit or to the Moon then multiple-stage firings are done to provide it a force in upward direction which is able to create an acceleration in it due to which its velocity increases and it goes out in spite of the Earth's gravitational pull.

Conclusion

Acceleration is the rate of change of velocity of a body and for that, a suitable force is required to be applied to the body. Why we are telling a suitable force is that sometimes the mass of the body might be more and a small force will not be able to move it and hence there is no question of acceleration in the body. If we try to push a big boulder or rock alone then nothing would happen. The force should be sufficient to move it and thereafter if the force is maintained then only the body would gain velocity leading to acceleration.

Frequently Asked Questions

If we increase the force on a body then will it's acceleration also increase?
Yes. The acceleration is proportional to the applied force and if we increase the force, acceleration would increase. This is known as famous 'Newton's second law of motion' which says that the acceleration of an object is directly proportional to the net force exerted on it and inversely proportional to the object's mass.
If we increase the force on a body then will it's acceleration also increase?
Yes. The acceleration is proportional to the applied force and if we increase the force, acceleration would increase. This is known as famous 'Newton's second law of motion' which says that the acceleration of an object is directly proportional to the net force exerted on it and inversely proportional to the object's mass.
When a rocket is fired from Earth to go to Moon why it does not stop due to friction of atmosphere or gravity of Earth?
Atmosphere is only for a very very small distance and the rest of the distance between the Earth and Moon is void of any atmosphere so once the rocket is out of the Earth's atmosphere there is no problem of friction. Moreover, the gravitational pull of Earth reduces as the rocket goes away and that is also not significant. So the rocket will move on with the acquired high speed.
If a body is moving at constant velocity then its acceleration is zero. Does it mean that there is no force applied on it?
Even if the body is moving with a constant velocity, some force will be required to maintain its velocity otherwise it would stop due to the frictional forces. For example, if a car is moving on a road with zero acceleration, then the engine would be pushing it a bit to compensate for the friction between the road and the car tyres.


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