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The Rate of Change of Velocity of an Object

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Last updated date: 29th May 2024
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What is Acceleration?

The word acceleration means the change of speed or we can say that change of velocity. A change in velocity is called acceleration. So basically, when velocity is changing, the term acceleration can be used and just like velocity, acceleration is also a vector quantity. It means acceleration has a magnitude and a direction.


Fundamentals of Acceleration

Mathematically, we express acceleration as the final velocity of an object minus the initial velocity of an object divided by the time interval in which the velocity has changed. Acceleration exists due to changes in velocity. The SI unit of rate of change of velocity is $\dfrac{m}{{{s^2}}}$ and it is a vector quantity. So, it has magnitude and direction also.


Positive Acceleration and Negative Acceleration

The formula for acceleration is the change of velocity divided by time duration. So, the formula for the rate of change of velocity can be defined as below:


$a = \dfrac{{v - u}}{t}$

where $v$ is the final velocity. This is the velocity at the end of the time duration.

$u$ is the initial velocity which is the velocity at the beginning of time duration.

$t$ is the total time taken.


The above formula can be positive or negative. That depends on whether the velocity is increasing or decreasing. If the velocity is changing positively, then the acceleration would become positive. In other words, we can say that the object is accelerating. That means, if velocity increases with time, acceleration will be positive. If the velocity is decreasing, then we can say that the value of acceleration would be negative. In this situation, we can say that it is a negative acceleration or we can call it retardation. Acceleration is taken to be negative, if it is opposite to the direction of velocity. That means, if velocity decreases with time, then we can say that acceleration will be negative.


From the above points, we can conclude that if velocity continuously increases, then the acceleration is called positive acceleration and when velocity continuously decreases, then the acceleration is defined as negative acceleration. When velocity is constant, then the acceleration is called zero acceleration.


Types of Acceleration

There are two types of acceleration:


Uniform Acceleration: If velocity increases at a constant rate, then the acceleration is called uniform acceleration. An object is said to be in uniform acceleration, if its velocity increases or decreases, but the amount of increase or decrease remains the same for equal amounts of time. In other words, we can say that acceleration remains constant in uniform acceleration.


Non-Uniform Acceleration: An object is said to be in non-uniform acceleration, when an object increases or decreases its velocity by unequal amounts in equal amounts of time. The best example to understand is riding a bike in traffic. In traffic, sometimes we have to speed up, sometimes we have to apply brakes and stop, sometimes we move at constant speed. So, this type of motion we can describe as non-uniform motion. This is the example of non-uniform acceleration that we feel in our daily life.


Solved Examples

1. The coin is thrown up from the ground with a velocity of $49\dfrac{m}{s}$ and after 5 seconds it comes to halt. Find the value of acceleration.

Ans: Given, Initial velocity $u = 49\,\dfrac{m}{s}$

Time taken is $t = 5\sec $

Here, we are throwing the coin up from the bottom, so the final velocity will become zero.

Here, we will use the formula $a = \dfrac{{v - u}}{t}$ and substituting the values, we will get

$a = \dfrac{{0 - 49}}{5} = - 9.8\,\dfrac{m}{{{s^2}}}$

So, the value of acceleration is $a = - 9.8\,\dfrac{m}{{{s^2}}}$.


2. An object dropped from a height falls with a constant acceleration of $10\dfrac{m}{{{s^2}}}$. Find its speed 5 seconds after it was dropped.

Ans: Given, acceleration $a = 10\,\dfrac{m}{{{s^2}}}$

Initial velocity of an object $u = 0\,\dfrac{m}{s}$

$t = 5\sec $

Here, we will use the formula $a = \dfrac{{v - u}}{t}$

$10 = \dfrac{{v - 0}}{5}\\ \therefore v = 50\,\dfrac{m}{s}$

Hence, the speed is $50\dfrac{m}{s}$.


Interesting Facts

  • The velocity versus time graph explains us about the acceleration of the object which is a vector quantity.

  • Gravity and force were explained by Sir Isaac Newton. He gave us three laws of motion which play an important role in Physics.

  • The acceleration versus time graph gives us the knowledge about change in velocity of an object.


Conclusion

In simple words, we can say that acceleration is used to denote the change in velocity with time. Negative acceleration is called de-acceleration or retardation. Acceleration remains constant in uniform acceleration. Whenever velocity increases by equal amounts or decreases by equal amounts in equal intervals of time, we can say that the object is uniformly accelerating.

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FAQs on The Rate of Change of Velocity of an Object

1. What is the difference between distance and displacement?

Here are a few points which show the difference between distance and displacement.

  • The actual path length between initial and final position is called distance. The shortest path length between initial and final point is called displacement. 

  • Distance is a scalar quantity. So, it has only magnitude. Displacement is a vector quantity. So, we can say that displacement has magnitude as well as direction. 

  • For the moving object, distance can never be equal to zero. Displacement can be zero. 

  • Distance travelled by an object per unit time is called speed. Displacement travelled per unit time is known as velocity. 

2. Give examples of acceleration in our everyday life.

When we throw a ball up, we are giving it some speed. So, the initial speed is greater than zero. The earth’s gravity is constantly pulling the ball down. So, the speed of the ball decreases. At the highest point, the speed of the ball will become zero. So, the ball going in an upward direction is a case of retardation. When the ball comes down from the top, the speed of the ball increases. So, we can say that the ball is accelerating. In other words, we can say that the ball going up is a case of retardation and the ball coming down is a case of acceleration. These are examples of acceleration in our everyday life.

3. Explain uniform circular motion with a few examples.

When an object moves in a circular path with constant speed, the motion of an object is known as uniform circular motion. The ball moving in a circle at a constant speed is an example of uniform circular motion. Here, the speed of the ball remains constant in this case but velocity is changing because the direction of the ball changes. In this case, we can say that this is an example of accelerated motion and also this type of motion is known as uniform circular motion. A merry go round and the blades of a fan are also examples of uniform circular motion.