To study velocity, acceleration, and the differences between them, first, a detailed study about the concept of motion is necessary. Not only that but also other basic definitions like scalar and vector quantities, expressing units, and so on should be known. First, let us see the motion of an object, which is also said as displacement.
The motion of an object
Consider an object moving from a fixed known point (as well as its position) with respect to its external influence, then the object is said to have undergone a motion.
Different types of motion
There are four types of motion. They are rotary, oscillatory, reciprocate, and linear. In all these types, the motion is set to happen with respect to time. Though the motion variation is slight, they all have a different notion. For example, for rotational motion, the displacement is called angular displacement and likewise for velocity, angular velocity, and so on.
Scalar and Vector quantities
Scalar quantities
A scalar quantity is the measure of a quantity which is one-dimensional, i.e., only its magnitude; for example, temperature, work, mass, and so on.
Vector quantities
A vector quantity is the measure of a quantity which is two-dimensional, i.e., both its magnitude and direction; for example, displacement, velocity, acceleration, and so on.
Units
A unit of measurement is the definite magnitude of a quantity. All measurements and their expression of the units are followed based on the International System of Units. There are seven basic units. They are as follows:
S.No. | Physical Quantities | SI Units |
1 | Length | metre (m) |
2 | Mass | kilogram (kg) |
3 | Time | second (s) |
4 | Electric current | ampere (A) |
5 | Temperature | kelvin (K) |
6 | Luminous intensity | candela (cd) |
7 | Amount of substance | mole (mol) |
Other sets of quantities are there, which are called derived quantities. They are a combination of seven basic units. Simply, they are derived from the fundamental quantities. Say, for example, the unit of force is m/s2 or ms–2 or Newton, abbreviated as N. Here “m” is the abbreviation of metre of the physical quantity length and “s” is the abbreviation of the second of the physical quantity time. Another example of a derived quantity is density. It is expressed as kg/m3 or kgm–3. Here, “kg” is the abbreviation of kilogram of physical quantity mass and “m” is the abbreviation of metre of the physical quantity length.
The displacement of an object is defined as the vector difference between the starting point to the ending point of a displaced object.
Displacement is not necessarily the same as distance travelled every time.
Displacement d = P – O = x m (m, unit of length)
Definition of velocity
The rate of change of displacement is velocity. When an object is moving in a specific direction with respect to time, it is said to be velocity, i.e., the quantity that specifies both distance and time is called velocity. The velocity of an object can be changed by changing the speed, direction, or both of that object.
In other words, it is defined as the displacement produced per unit time.
Velocity = Displacement / Time
= x / t
Where x is the distance travelled in a given direction, i.e., displacement. It is calculated as the difference between the positions.
x = Final point – Initial point
= v – u
t, time taken to travel the distance.
V = d / t
Velocity V is calculated as the change in displacement with respect to time. It is a vector quantity as it is dependent on both magnitude and direction.
For example, travelling in a car at a speed of 20 m/s towards the north in 2 minutes; this explains that the car moved with what speed, in what direction, and the time took for this displacement.
Hence, velocity is a vector quantity. Vector quantity involves not just the magnitude but also the direction, i.e., two-dimensional. SI unit of velocity is m/s or ms–1.
Definition of Speed
Speed is the distance travelled by an object in a given time. Speed is a scalar quantity as it expresses only the magnitude and not the direction.
Speed = Distance / Time
Velocity and speed are similar with respect to the motion of an object. In simple words, velocity is the speed with direction. Velocity includes direction with displacement whereas speed includes only distance travelled.
Definition of Acceleration
The common use of the word “acceleration” refers to moving or increasing with high speed. But the actual meaning is the change of speed, i.e., change of velocity (by increasing or decreasing the speed). The rate of change of velocity is acceleration.
As we have seen before, velocity is said to be the speed with direction. In other words, when there is a change in velocity, consequently the acceleration exists.
For example, consider a pebble dropped into the water. When the pebble is dropped, its initial speed is zero, when it hits the water, its speed increases due to the Earth's gravity. So, the water splashes up. Therefore, acceleration is defined as the rate of change of velocity. If the velocity of a body is changed from “u” to “v” in time “t”, then acceleration is given as follows.
Acceleration = Change in velocity / Time taken
= Final velocity – Initial velocity/time taken
A = d(u–v) / dt
As it has both magnitude and direction, it is a vector quantity. SI unit of acceleration is m/s2 or ms–2.
Difference between Velocity and Acceleration
Velocity | Acceleration |
Velocity is the rate of change of displacement. | Acceleration is the rate of change of velocity. |
Velocity is a vector quantity because it consists of both magnitude and direction. | Acceleration is also a vector quantity as it is just the rate of change of velocity. As velocity is a vector quantity, obviously, acceleration is also. |
Velocity may be positive or negative or zero. | Acceleration may be positive or negative. It cannot be zero as it is defined as the change in velocity or speed. This explains that there should be some motion for acceleration. |
SI unit is m/s or ms–1. | SI unit is m/s2 or ms–2. |
Formula for velocity = displacement/time | Formula for acceleration = velocity/time |
These are the differences between velocity and acceleration.
Velocity is the rate of displacement of an object. It is measured in m/s. Acceleration is the rate of change of velocity of an object. It is measured in m/s2. They are both vector quantities i.e. both magnitude and direction are required to fully specify them.
| Vector | Vector |
| Velocity | Displacement |
| Velocity, time | Distance, time and direction of motion |
| Velocity/time | Displacement/time |
| m/s2 | m/s |
| a=v/t | v=d/t |
Velocity is the change in position (location) of an object per unit time. e.g., a bus traveling at a velocity of 60 miles per hour from North to South. The SI unit of velocity is meters per second (m/s). In general, it is important to indicate the direction of motion when specifying the velocity. In other words, it is a vector quantity, as opposed to a scalar quantity that would specify the speed without mentioning the direction.
Acceleration is the change in velocity of an object per unit time. The SI unit of acceleration is meters per second per second i.e., meters per second squared (m/s2). e.g., the acceleration of a free-falling object on Earth is 9.8 m/s2 because of Earth's gravity.
Calculating velocity
Velocity is the distance an object has moved in a particular direction within a specified time interval. If the object returns to its starting position then the velocity is zero.
This video explains how to calculate average velocity over a constant acceleration:
Calculating acceleration
Instantaneous acceleration is the change in velocity
Average acceleration over a period of time is the change in velocity (
Therefore the SI unit of acceleration is meter per second per second, i.e. meter per second squared (m/s2).
This video explains how to calculate acceleration using the example of a Porsche.
Types of Acceleration
If an object is moving at constant speed in a circular motion -- such as a satellite orbiting the earth -- it is said to be accelerating because change in direction of motion means its velocity is changing even if speed may be constant. (See Speed vs Velocity) This is called centripetal (directed towards the center) acceleration. On the other hand, if the direction of motion of the object is not changing but its speed is, this is called tangential acceleration.
If the direction of acceleration is in the same direction as that of velocity then the object is said to be speeding up or accelerating. If the acceleration and velocity are in opposite directions then the object is said to be slowing down or decelerating.
An example of constant acceleration is the effect of the gravity of earth on an object in free fall.
Velocity and Acceleration in a Pendulum
When a pendulum swings from side to side, its velocity and acceleration vary — both in magnitude and in direction — at each point during the motion.
The magnitude of velocity of a pendulum is highest in the center and lowest at the edges. On the other hand, the magnitude of its acceleration is highest at the edges and lowest at the center.
Practical applications
- Applications of velocity in real life are to calculate the time taken for a storm to reach the coastline, the time taken for a satellite to reach moon and so on.
- Accelerometers are used to measure acceleration of an object. Measurement of acceleration of a vehicle enables to evaluate overall vehicle performance and response.
- Detection of rapid negative acceleration of a vehicle is used to detect vehicle collision and deploy airbags.
- The measurement of acceleration is also used to measure seismic activity, inclination and machine vibration.
- Vibration monitoring is used in industries such as automotive manufacturing, machine tool applications, pharmaceutical production, power generation and power plants, pulp and paper, sugar mills, food and beverage production, water and wastewater, hydropower, petrochemical and steel manufacturing.
References
- Follow
- Share
- Cite
- Authors
Share this comparison:
If you read this far, you should follow us:
"Acceleration vs Velocity." Diffen.com. Diffen LLC, n.d. Web. 2 Nov 2022. < >