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# Acceleration Formula

Last updated date: 12th Aug 2024
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## What is Acceleration?

When a stationary car starts suddenly, we get pushed up backward, and when brakes are applied, we get pushed forward against our seat, or when our car takes a sharp right turn, we get pushed towards the left. We experience these situations because our car is accelerating.

Simply when there is a change in Velocity, there will be Acceleration. Let’s understand the concept of Acceleration with illustrative examples.

Let’s suppose I have a car moving with a constant Velocity of 90 kmph along a straight line. I can see a helicopter flying at roughly a speed of 20,000 kmph. If I were to ask you that in these two cases, where do you find the Acceleration? Your answer will be surely no because both are moving at a constant pace, so no Acceleration in both cases.

Now, if I ask you that Acceleration is equal to high speed. What will be your answer? You may say yes, but that’s not true for sure.  Want to know why?  It’s because Acceleration is the rate of change of Velocity. Now, let’s understand the Acceleration formula.

### General Formula of Acceleration

We already know that Velocity is a speed with direction; therefore, it is a vector quantity. The Acceleration ‘a’ is given as:

$a = \frac{\text{Change in Velocity}}{\text{Time Taken}}$

This formula states that the rate of change in Velocity is the Acceleration, or if the Velocity of an object changes from its initial value ‘u’ to the final value ‘v’, then the expression can be simply written as:

$a = \frac{(v - u)}{t}$

## Acceleration Formula in Physics

In Physics , Acceleration is described as the rate of change of Velocity of an object, irrespective of whether it speeds up or slows down. If it speeds up, Acceleration is taken as positive and if it slows down, the Acceleration is negative. It is caused by the net unbalanced force acting on the object, as per Newton’s Second Law. Acceleration is a vector quantity as it describes the time rate of change of Velocity, which is a vector quantity. Acceleration is denoted by a. Its SI unit is $\frac{m}{s^{2}}$ and dimensions are $[M^{0}L^{1}T^{–2}]$.

If $v_{0}, v_{t}$ and t represents the initial Velocity, final Velocity and the time taken for the change in Velocity, then, the Acceleration is given by:

$\overrightarrow{a} = \frac{\overrightarrow{v_t} - \overrightarrow{v_0}}{t}$

In one dimensional motion, we can use;

$a = \frac{v_t - v_0}{t}$

### Acceleration Formula

If $\overrightarrow{r}$represents displacement vector and $\overrightarrow{v} = \frac{\overrightarrow{\text{d}r}}{\text{d}t}$ represents the velocity, then;

### Acceleration:  $\overrightarrow{a} = \frac{\overrightarrow{\text{d}v}}{\text{d}t} = \frac{\overrightarrow{\text{d}^{2}v}}{\text{d}^{2}t}$

In one dimensional motion, where x is the displacement, and $v = \frac{\text{d}r}{\text{d}t}$ is the Velocity, then;

### $a = \frac{\text{d}{v}}{\text{d}t} = \frac{\text{d}^{2}x}{\text{d}^{2}t}$

Example 1:

A car starts from rest and achieves a speed of 54 $\frac{km}{h}$ in 3 seconds. Find its Acceleration?

Solution:  $v_0$ = 0, $v_t$ = 54 $\frac{km}{h}$ = 15 $\frac{m}{s}$, t = 3s, a = ?

Acceleration:

$a = \frac{v_t - v_0}{t} = \frac{15 - 0}{3} = 5 \frac{m}{s^{2}}$

Example 2:

A body moves along the x- axis according to the relation $x = 1 – 2 t + 3t^{2}$, where x is in meters and t is in seconds. Find the Acceleration of the body when t = 3 s

Solution:

We have: $x = 1 – 2 t + 3t^{2}$

then; Velocity $v = \frac{\text{d}x}{\text{d}t} = -2 + 6t$

Acceleration:  $v = \frac{\text{d}v}{\text{d}t} = 6 \frac{m}{s^{2}}$.

(We see that the Acceleration is constant here. Therefore, at t = 3s also, its value is 6  $\frac{m}{s^{2}}$).

### Solved Questions Using Acceleration Formula:

1. What will be the Acceleration of a Car if it Slows from 90 $\frac{km}{h}$ to a Stop in 10 sec?

Here, u = 90 $\frac{km}{h}$ = $\frac{90 \times 5}{18} = 25 \frac{m}{s^{2}}$ because initially it was moving at a speed of 90 kmph then reached zero.

Final Velocity ‘v’ = 0 kmph, and t  = 10 seconds

Now, applying the formula here:

$a = \frac{(0 - 25)}{10} = (-) 2.5 \frac{m}{s^{2}}$

2. A Girl Starts her Motion in a Straight Line at a Velocity of 30 $\frac{m}{s}$, her Velocity is Changing at a Constant Rate. If She Stops after 60 s, What is her Acceleration?

Answer: Here, the initial Velocity of a girl was 30 $\frac{m}{s}$ and stops, so her final Velocity will become 0 m/s. Now, the deceleration or retardation occurs, which is just the opposite of Acceleration and it can be determined as:

$a = \frac{(0 - 30)}{60} = (-) 0.5 \frac{m}{s^{2}}$

Question 3: A Car Moves in a Circular Track with a Constant Velocity; will it Experience Acceleration?

Answer: Here, the speed is constant; however, the direction is continuously varying, which means the Velocity is also varying. It states that the car will experience Acceleration.

### How to prepare for a test on Acceleration using Vedantu

• You can log onto Vedantu and then go through the study material that’s present

• You can click on Acceleration Formula with examples and solved problem

• After going through this study matter, the concepts will get much clearer

• You can also make notes of the above by writing down the important points

• Carefully observe the solved examples

• The matter will have ensured that you are preparing well for the exams

### Why choose Vedantu?

Vedantu is a top e-learning platform that only keeps the best study material on its website. It is extremely dependable since all students bank on it before they sit down for revisions or tests. The study material on it is free of cost and can be downloaded and then gone through in the offline mode as well. You should choose Vedantu if you need to be smartly prepped up before your tests and learn all the complex concepts.

## FAQs on Acceleration Formula

1. Where can I find sums on Acceleration?

You can find ample examples and sums on Acceleration if you choose to read Acceleration Formula with examples and solved problems on Vedantu. This has a detailed description of what Acceleration is, what its examples are, how it's related to speed and direction.  You will find the kind of sums that will come for the tests here so that you can practice them and secure good marks. Do not skip reading any part as that might cause problems with understanding the concepts later on.

2. How do I clear my concepts related to Velocity and speed?

You should understand the very basics of what each is so that you can answer questions when they are asked. Go through Acceleration Formula with examples and solved problems available on this page on Vedantu as this is the ideal guide for those who are looking to clear their concepts.

Velocity is the speed with direction. The rate of change in Velocity would be termed Acceleration.  Understanding this is key to solving the sums that come from this chapter and topic. You should go through the entire description along with its formulae and examples. Practice a few sums and then assess your understanding.

3. When a car suddenly halts, why do we get pushed forward against our seat?

As a car suddenly stops,  we tend to get pushed forward as our car starts accelerating. As there is a change in the speed with direction (Velocity), Acceleration occurs.  More about this is provided if you go to  Acceleration Formula with examples and solved problem. This can be found on Vedantu and contains all the relevant details that need to be known. It has explained everything in an extremely simplified manner with the help of examples and is an ideal guidebook for those who are looking to clear their concepts related to Acceleration.

4. Is Acceleration the same as very high speed?

You may be partially correct in stating so but not entirely. Acceleration is more essentially the rate of change of Velocity.  You can read from Acceleration Formula with examples and solve problems on Vedantu and then understand better. It has the description of Acceleration along with its sums and a lot of examples. It has a comprehensive description of the topic and its related concepts so that students do not get confused while learning about the topic. Acceleration as a concept is crucial for the higher classes as the Science and Maths study material that they come across then, will be based on these.

5. Can I skip the chapter and the sums on Acceleration when I am studying?

You should not skip anything at any point in time as it could lead to securing lower grades overall. If you have any queries regarding the concepts on Acceleration and its related problems, you can refer to Acceleration Formula with examples and solved problems on Vedantu’s platform. This will clear all your doubts so that you do not feel tempted to skip this chapter just because it's slightly tricky. Once you have completely scanned this page, you will be able to solve the sums that come for your tests and be more confident in tackling questions that come from the chapter.