Acceleration- Formula, Unit, Definition and Meaning

Acceleration

Acceleration is an important concept in physics and is used to define motion. Acceleration is defined as the rate of change in velocity which implies that an object is said to be accelerating when the velocity of the object is increasing or decreasing. Acceleration has both magnitude and direction which make it a vector quantity. The magnitude of the acceleration of an object is the combination of two factors net resulting force and the mass of the object, as per Newton’s Second Law of Motion. Let us understand in detail more about acceleration, its units, types, and graphs.

What is Acceleration?

Acceleration is defined as the rate of change of velocity of an object concerning time. When the velocity of an object is changing, it is said to be accelerating.

Acceleration can also be defined as the rate of change in velocity and the change over time. Acceleration can be positive, negative, or zero.

• Positive Acceleration occurs when the velocity of the object increases with time.
• Zero Acceleration occurs when the velocity is neither decreasing nor increasing it is zero.
• Negative Acceleration occurs when the velocity decreases with time. It is also known as retardation.

Acceleration Formula

The change in the velocity of an object in motion is defined as “v-u” where v is the final velocity and u is the initial velocity. Therefore, the acceleration of an object with initial velocity ‘u’ and final velocity ‘v’ and time took ‘t’ is

Acceleration = Change in Velocity /Time taken

Which gives the formula

a = (

S. I Unit of Acceleration

Acceleration is a vector quantity as it has both magnitude and direction. It is denoted by a. The unit of acceleration is meters per second squared which is m/s². The dimensional formula of acceleration is [M⁰ L¹ T^-2].

Types of Acceleration

There are different types of Acceleration, namely uniform, non-uniform, average, and instantaneous, acceleration.

1. Uniform Acceleration

When the velocity of an object changes in equal amounts during the same time intervals, then the object is said to be in uniform acceleration. During uniform acceleration, the direction and the magnitude do not change with time.

Example: motion of a car with constant velocity or a ball rolling down a slope.

2. Non-uniform Acceleration

Non-uniform acceleration is also known as variable acceleration. In variable acceleration the velocity of the object changes by varying amounts during the same time interval. During non-uniform acceleration, the magnitude and direction both change with time.

Example: A car changes its speed after every kilometer it travels.

3. Average Acceleration

When the object changes its velocity for a particular specified time interval it is said to have average acceleration. The formula for calculating the average acceleration is given below.

A_v =∆v/∆t or a_v = (v_f-v_i) / (t_f -t_i)

Here, v_f is the final velocity

v_i is the initial velocity

t_i is the initial time

t_f is the final time

4. Instantaneous Acceleration

Instantaneous acceleration is defined as the ratio of change in velocity during a given time interval such that the time interval goes to zero. To calculate the instantaneous acceleration, the average velocity can be calculated between two points in time separated by ∆t and ∆t approaches zero. The result obtained is the derivation of the velocity function v(t) which is the instantaneous acceleration, which when mathematically written gives

a(t) =  v(t)

Acceleration Velocity Time Graph

The curves indicate the velocity-time graph, where time is plotted along the x-axis, and velocity is plotted along the y-axis.

1. When the velocity of an object is constant or Zero Acceleration.

2. When the object is moving with a constant acceleration and the initial velocity is zero.

3. When an object is moving with constant retardation

4. When the object moves with non-uniform acceleration and the initial velocity is zero.

5. When the acceleration is decreasing and increasing.

Difference between Acceleration and Velocity

Solved Examples of Acceleration

1.If a car accelerates from 5 m/s to 10 m/s in the 20s. Calculate its acceleration.

Ans. Given,

Initial Velocity, u = 5 m/s

Final Velocity, v = 10 m/s

Time Taken, t = 20 s

Acceleration, a= (v-u)/t

= (10m/s – 5m/s) / 20

= 0.25 m/s²

2. If a truck is going at a speed of 100 km/h is slowed down and brought to 70 km/h in 5s. Calculate the retardation of the truck?

Ans.  Given,

Initial Velocity, u = 90 m/s or 90 x  = 25 m/s

Final Velocity, v = 72 m/s or 72 x  = 20 m/s

Time Taken, t = 20 s

Acceleration, a= (v-u)/t

= (20m/s – 25m/s) / 20

= -0.25 m/s²

3. If a car is moving from rest and then accelerates uniformly at 8.2 m/s² for 10s. Find the velocity of the train in 10s.

Given,

Initial Velocity, u = 0 m/s (car is in rest)

Time Taken, t = 10 s

Acceleration, a= 8.2 m/s²

v = u + at

= 0 + 8.2 x 10

= 82 m/s

Acceleration- FAQs

1. What is the average acceleration over time?

Ans. The average acceleration over time ka is defined as the total change in velocity in given intervals of time divided by the total time taken for the change.

2. What is Acceleration due to gravity?

Ans. The acceleration due to gravity is defined as the acceleration experienced by the earth’s gravitational pull.

3. What do you understand by Centripetal Acceleration?

Ans. Centripetal Acceleration is defined as the acceleration points toward the center of the curvature since the velocity is continuously changing and acceleration is present.

4. How acceleration is related to force?

Ans. Acceleration is directly proportional to the force applied to an object with constant mass.

5. Why acceleration is a vector quantity?

Ans. Acceleration is a vector quantity because it is related to both magnitude and direction.