Unit of Acceleration

Last Updated : 12 Mar, 2024

Unit of Acceleration is meter per second square or m/s². Acceleration is the rate at which the velocity of a body changes. The most commonly used units of acceleration are meters per second square (m/s²) and kilometer per hour square (km/h²).

In this article, we will learn the definition of acceleration, the unit of acceleration, units in various systems, sample problems, and frequently asked questions related to the unit of acceleration.

unit-of-acceleration

Table of Content

What is Unit of Acceleration?
SI unit of Acceleration
Unit of Acceleration in Other Systems
C.G.S. Unit of Acceleration

What is Acceleration?

Acceleration is a measure of the rate at which the velocity of a body changes. It is a vector quantity which means it has both magnitude and direction. It can be positive, zero or negative.

The definition of acceleration is written as follows,

Acceleration is the change of velocity with respect to time.

Acceleration Formula

Acceleration is calculated as the ratio of change in velocity and time taken for the change. Hence, the formula for acceleration is written as,

a = v/t

where, a is the acceleration of the body,

v is the velocity of the body and

t is the time taken.

Acceleration of a body can also be expressed as :

a = Δv/t

where, Δv is the change in velocity.

What is Unit of Acceleration?

Unit of Acceleration is the measurement of the magnitude of acceleration according to a defined standard or convention as set by the International System of Units. As the formula of acceleration is change in velocity per unit time taken, unit of acceleration would be the unit of velocity per unit time taken.

For convenience, various systems of units have been adopted and units can be converted from one system to another by multiplication with some numerical factor. The SI unit of acceleration is meter per second square. The unit of acceleration depends upon the units of velocity and time.

Dimensional formula for Acceleration

The dimensional formula for acceleration is [M⁰L¹T^-2]. It can be derived using the formula of acceleration, i.e. Acceleration = Change in Velocity/Time

Substituting the dimensions of velocity and time, we get,

Dimension of Acceleration = [M⁰L¹T^-1] / [M⁰L⁰T¹]

Dimension of Acceleration = [M⁰L¹T^-2]

SI unit of Acceleration

S.I. unit of acceleration is meters per second square abbreviated as m/s². It can be derived as follows:

S.I. unit of velocity= meter/second(m/s)
S.I. unit of time= second(s)

We know that,

Acceleration = Change in Velocity/Time

Hence,

SI unit of acceleration = SI unit of Velocity/SI unit of Time

SI unit of acceleration = (meter/second)/(second)

SI unit of acceleration = (m/s)/(s) = m/s²

Thus, we obtain SI unit of acceleration = ms^-2 or m/s².

C.G.S. Unit of Acceleration

C.G.S. system of units stands for Centimeters (length), Grams (mass), and Seconds (time). Acceleration is rate of change of velocity with respect to time. In CGS system, unit of velocity is cm/s. Thus, unit of acceleration in CGS system would be cm/s². Hence, we have derived the CGS unit of acceleration as follows:

CGS unit of Velocity: cm/s
CGS unit of Time: s

CGS unit of Acceleration = CGS unit of Velocity / CGS unit of Time

CGS unit of Acceleration = (cm/s) / s

CGS unit of Acceleration = cm/s²

Other Units of Acceleration

Unit is a standard measurement of a physical quantity that are used to express the size or magnitude of any physical quantity in relation to a standard reference. There are different units chosen for the measurement of same physical quantity for its convenient representation in terms of magnitude. Different units of acceleration are discussed as follows:

Feet per Second square

Feet per Second square is an unit of acceleration in FPS system, i.e. Feet (length), Pound (mass), and Second (time). It represents the acceleration in which velocity changes by 1 foot in 1 second. 1 foot is 0.3048 meters.

Thus, 1 ft/s² is the acceleration in which velocity changes by 0.3048 m/s in 1 second.

Gal Unit of Acceleration

Gal unit of acceleration is 1 cm/s². It is named after the scientist Galileo Galilei. It is commonly used in measurements related to acceleration due to gravity.

The acceleration due to Earth’s gravity at its surface is taken as 976 to 983 Gal. 1 Gal is equal to 0.01 m/s². It is same as the unit of acceleration in CGS system.

Standard Gravity

Standard Gravity is the value of acceleration due to gravitational force experienced by an object on Earth’s surface. It is taken as a constant and defined as 9.80665 m/s². In CGS system, it is 980.665 cm/s².

Planck Acceleration

Planck Acceleration is the acceleration required for an object which is initially at rest to attain the speed of light in Planck unit time. Planck time is defined as 5.391 x 10⁻⁴⁴ seconds. The value of 1 unit of Planck Acceleration is thus obtained as 10⁵¹ m/s².

S.I. Unit of Angular Acceleration

Angular Acceleration is the rate of change of angular velocity with respect to time. Thus, SI unit of angular acceleration would be SI unit of angular velocity divided by the SI unit of time.

We know that, SI unit of angular velocity is rad/s and SI unit of time is s.

i.e. (rad/s)/s= rad/s²

Hence, SI unit of angular acceleration would be rad/s².

S.I. Unit of Centripetal Acceleration

Centripetal Acceleration is the acceleration of a body in circular motion. The force required for circular motion is given by the following expression,

F_c = mv²/r

Comparing it with F = ma, we get centripetal acceleration (a_c) as follows,

a_c = v²/r

Now, SI units of centripetal acceleration (a_c) would be (m/s)²/(m) or m/s².

S.I. Unit of Radial Acceleration

Radial acceleration acts along the radius of an object and directed towards its centre. A body in circular motion has two components of acceleration, i.e. radial and tangential directed towards center and tangent of the circle respectively.

Mathematically, it is defined as:

a_r = v²/ r

where v is angular velocity and r is angular displacement.

Hence, the unit of radial acceleration a_r can be given as:

Unit of a_r = (rad/s)²/rad [As SI unit of v and r is rad/s and rad respectively]

On solving we get,

Unit of a_r = rad/s²

Radial acceleration is also called normal acceleration. It has same units as that of angular acceleration, i.e. rad/s².

Conclusion

In conclusion, it can be said that unit of acceleration depends on the unit of velocity and unit of time as acceleration defines the rate of change of velocity with respect to time.

Thus, the SI unit of acceleration is m/s² as SI unit of velocity and time are m/s and s respectively.

Read More,

Unit of Current

System of Units

Solved Questions on Unit of Acceleration

Question 1: The velocity of an object changes from 18 km/h to 54 km/h in 20 seconds. Find out its acceleration in SI units.

Solution:

Here, we have,

Initial Velocity = 18 km/h and Final Velocity = 54 km/h

Time taken = 20 secs

Change in Velocity = (54-18) = 36 km/h

Converting the change in velocity to SI units, we get,

Change in Velocity = 36 x 5/18 = 10 m/s

We know that,

Acceleration = Change in Velocity/Time Taken

Acceleration = 10/20 = 0.5 m/s²

Thus, the acceleration of the object is found to be 0.5 m/s².

Question 2: A body is moving in a circle of radius 5 meters with a speed of 20 m/s. Find out it’s centripetal acceleration.

Solution:

Here, v = 20 m/s and r = 5 m

We know that,

Centripetal Acceleration (a_c) = v²/r

Thus, a_c = (20)²/5 = 400/5 = 80 m/s²

Hence, the value of centripetal acceleration is obtained as 80 m/s².

Practice Questions on Unit of Acceleration

Question 1: Find out the acceleration of a body whose velocity changes from 6 km/h to 18 km/h in 5 seconds.

Question 2: Acceleration due to gravity at surface of moon is one-sixth of that on earth. What would be the weight of a person on moon having a mass of 40 kg.

Question 3: Convert 18 km/h² to SI units.

Question 4: A body is in a circular motion with speed as 5 m/s in a circle having radius as 20 cm. Calculate the centripetal acceleration of the body.