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In this article, we have covered various topics for differentiating Acceleration and Velocity. You can learn about Acceleration and velocity which are discussed in the following article. There are various types of both Acceleration and Velocity that are discussed in the article. Before knowing about the advanced topics on Acceleration and Velocity, you have to understand some basic things about it.
The term ‘acceleration’ can be defined as the rate of change of velocity with time. It happens with respect to both speed and direction. The concept of acceleration was introduced by Italian Physicist Galileo Galilei and English Physicist Isaac Newton.
Velocity is defined by how quickly a motion takes place. It measures the rate and direction in which the position of an object changes. However, we must remember that velocity and speed are two different things that we will study further. Newton made this theory known to people. The word comes from the Latin word ‘Velox’, which means fast.
Read Also: Velocity Selector
| Table of Content |
Keyterms: Acceleration, Velocity, Time, Motion, Speed, Metre, Final velocity, Initial velocity, Unit of acceleration, Straight line, Time interval
What is Acceleration?
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Acceleration is the rate of change of velocity of an object with respect to time, in terms of speed and direction. It is a vector quantity by nature.
- An apple falling from a tree
- A car slowing down
- A cycle turning at the corner of the road
All of these above mentioned points bring about a change in the speed and direction and are therefore all examples of acceleration.
The SI unit of acceleration is metres/second2 or (m/s2).
Formula: a = (v – v0)/t
= Δv/Δt
Where,
a = acceleration, v is final velocity, v0 is initial velocity and t is time taken.
Check Important Notes for Speed Time Graph
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Current Electricity Detailed Video Explanation:
Read Also: Difference Between Distance and Displacement
Types of acceleration
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Uniform acceleration:
If a body is traveling in a straight line, and its velocity increases by equal amounts in exactly regular intervals of time, it is said to be uniformly accelerated. It is also called constant acceleration, because the object’s velocity is increasing at a constant rate.
If a car is moving at a certain speed in a straight line, then it suddenly slows down or even turns right or left, it loses its uniform acceleration. The moving car doesn't possess constant acceleration anymore.
Example of uniform acceleration is a free-falling body. Suppose, you fall off from a bridge or top of a building, this acceleration which takes place, is only because of gravity.
The equation for uniform acceleration can be denoted by,
S = ut + ½ at2 (this is known as the distance formula)
Where,
- u - The initial velocity of the body
- a - Acceleration of the body
- t - The time interval
Now, velocity becomes,
v = u + at
Where,
- v - The final velocity of the body
- u - The initial velocity of the body
- a - Acceleration of the body
- t - The time interval
Read More: Difference Between Kinetics and Kinematics
Non-Uniform acceleration
This motion is the opposite of uniform acceleration. A body is said to be moving in a non-uniform acceleration, if its velocity increases in irregular amounts, in regular intervals of time. Here, the change in velocity is not constant, it keeps changing. Also, the direction along with the magnitude of acceleration will change.
A car driving in heavy traffic, a kid in a cycle on an inclined road is all examples of a non-uniform acceleration.
Average acceleration
We know that acceleration means the rate of change of velocity. Average acceleration denotes a given time interval. It can be defined as the change in velocity for a particular time interval.
For example, if the velocity of a speeding bicycle increases from 0 to 120 cm/s in 6 seconds, then the average acceleration of the bicycle would be 20 cm/s2. It means, the velocity of the bicycle is increasing by 20 cm/s in each second.
Instantaneous acceleration
The acceleration of a body at any given instance is known as instantaneous acceleration. If the velocity decreases acceleration will become negative or retardation. Similarly, if velocity increases it will be positive acceleration.
Centripetal or circular acceleration
When a body is moving in a circular path, its acceleration is called centripetal acceleration. During its circular motion, its direction changes constantly which causes the velocity to change. As a result, a force of acceleration is produced and it is directed towards the center.
When you whirl a ball with a string, the ball is undergoing centripetal acceleration. Similarly, if you are sitting in a merry-go-round, and it's moving, it can also be called centripetal acceleration.
The equation for circular acceleration can be denoted by,
ac = v2/r
Where,
- ac = denotes centripetal acceleration
- v = velocity
- r = radius
- The SI unit for centripetal acceleration is m/s2.
Deceleration/ retardation
The deceleration can be called the opposite of acceleration. It reduces speed and is in the direction opposite to the direction of velocity. It can also be called negative acceleration.
It is denoted by putting a negative sign beside acceleration like, –a, where a signifies acceleration. This is to help identify the deceleration value.
The equation for deceleration can be denoted by,
Deceleration = (Final Velocity–Initial Velocity)/time taken
a = (v - u)/t
Also Read:
| Related Articles | ||
|---|---|---|
| Relative Speed | Average Acceleration Formula | Kinematics Equation |
| Distance and Displacement | Unit of Speed | Unit of Momentum |
What is Velocity?
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It's the rate at which an object changes its position with respect to time. Like acceleration, it is too a vector quantity. It can be described as how fast an action takes place or is done.
It should be kept in mind that speed and velocity are two different things. Speed is a scalar quantity.
The SI unit of velocity is m/s.
Formula,
V = Δx / Δt
Where, v = average velocity, Δx is displacement, and Δt is change in time.
Read Further: Unit of Vector
Types of velocity
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- Constant Velocity: A body or an object is said to have constant velocity, when it's moving in a straight line, without any change in its speed or velocity. There is no change in the direction. Constant velocity basically means that acceleration becomes 0. For example, a car moving on a straight road with a steady speed of 10m/s without changing direction can be called an example of constant velocity.
- Changing Velocity: When a moving object changes speed, or direction, or both, it is said to be undergoing a change in velocity. This can be called acceleration. Cars racing on the circular tracks undergo a change in their velocity. Heavenly bodies like meteors and comets can also be called as an example of changing velocity. Their speed and direction can change anytime because it is dependent on gravitational pull.
- Instant Velocity: Instantaneous velocity can be defined as the velocity of a moving body at any given instant of time. It is a bit similar to average velocity, but it is limited here. The time frame reaches 0 over here. This concept of velocity is popularly used in graphs.
Formula, v(t) = ddtx(t)
- Terminal velocity: When a body falls freely, it will gather more velocity, therefore more downward gravity pull. The acceleration will become 0 because of the resistance present in the atmosphere. This point, where both the resistance of air as well as the force/acceleration acting on the object, is called terminal velocity. Terminal velocity refers to the maximum speed/ velocity which an object can attain while free falling.
Read Important Notes for Derivation of Centripetal Acceleration
Difference between acceleration and velocity
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Following are the differences between acceleration and velocity:
| Acceleration | Velocity |
|---|---|
| Acceleration is the rate of change of velocity. | Velocity can be defined as the rate of change in displacement. |
| Acceleration can be positive, or negative. It cannot be 0. | Velocity can be positive, negative, or even zero. |
| Acceleration is also vector in nature. | Velocity is a vector quantity because it consists of both the magnitude and direction. |
| It determines the rate at which a moving object’s velocity changes with time. | It determines the direction and how fast an object moves. |
| Acceleration is denoted by a. | Velocity is denoted by v. |
| The unit of measurement for acceleration is signified by meter/second or m/s. | The unit of measurement for velocity is signified by meter/second2 or m/s2. |
| Formula = velocity/time | Formula = displacement/time |
Read More: Ampere’s Circuital Law
Things to Remember
Following are some points which should be cleared by the readers:
- Acceleration is the rate of change of velocity with time, in respect to speed and direction. Velocity is the rate of change of displacement with respect to time. Both of them happen to be vector quantities. The SI unit of acceleration is m/s2 whereas the SI unit of velocity is m/s.
- There are five kinds of acceleration motions. These are uniform acceleration, non-uniform acceleration, average acceleration, instantaneous acceleration and centripetal acceleration. Velocity has been classified into four broad categories. These are constant velocity, changing velocity, instant velocity and terminal velocity.
- It is because of the contribution of Galileo Galilei and Issac Newton that we have come to acquire all this knowledge about acceleration and velocity. They both were physicists. Galileo actually came up with this theory by looking at some rocks rolling down a hill. Then the idea of accelerated motion was introduced.
- The most important factor behind acceleration is the gravity pull of the earth. It elevates the acceleration, thereby causing the velocity to increase. Speed and velocity are different things. Speed is a scalar quantity. The fastest speed in the entire universe happens to be of light. The speed of light is 299,792,458 meters per second.
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Sample Questions
Ques: A moving car gradually slows down and comes to a position of rest from 114 km/h in just 20 seconds. What is acceleration? (3 marks)
Ans: We know that,
The initial velocity, u = 114 km/h
U = 100 * 5/18 (converting)
U = 30 m/s
Final velocity, v = 0, because it came to a position of rest.
Time = 20 seconds
a = (v - u)/t
a = (0-30)/20
a = -1.5m/s2
This can also be called negative acceleration or retardation.
Ques: Are speed and velocity the same things? (2 marks)
Ans: No, they are not the same thing. Speed is the rate at which an object moves or covers a distance, while velocity is the rate at which an object changes its direction. Speed is a scalar quantity while on the other hand velocity is a vector quantity. The magnitude of speed can never be negative or 0 whereas magnitude of velocity can be positive, negative and even 0.
Ques: A bike moves in a straight line at constant acceleration. Velocity of the bike grows from 20 m/s to 50 m/s. What is the distance travelled by the bike? (2 marks)
Ans: Applying the formula of average velocity and displacement,
Average velocity = (v1 + v2)/2 × Δt
= (20 + 50)/2 ×10
= 350 meters
Ques: A boy starts riding a bicycle with a velocity of 30 m/s. He ends his ride in time duration of 8 seconds at a velocity of 26 m/s. Find the average acceleration. (3 marks)
Ans: We know that,
Initial velocity, v1 = 30m/s
Final velocity, vf = 26m/s
Time taken, Δt = 8 seconds
Therefore,
Acceleration, a = (vf – v1)/Δt
a = (-26-30)/8
a = (-56)/8
Acceleration = -7m/s2
Or negative acceleration = 7m/s2.
Ques:A woman travels a distance of 60m in just 5 seconds. Her acceleration is 4m/s2. Calculate the initial velocity. (3 marks)
Ans: We know that,
Δx=60m
Δt=5 seconds
a=4m/s2
v0=?
Δx = ½at2+ v0 t
Δx = ½ * 4 * 52 + v0 5
60 = 50 + v0 5
V0 = 2 m/s
Ques: A man takes a rock and throws it standing on a cliff. It falls for 10 seconds before it hits the ground. The acceleration due to gravity g = 9.80 m/s2. Calculate the velocity of the rock just before hitting the ground. (3 marks)
Ans: We know that,
Initial velocity, vi is 0.
Time = 10 seconds
G = 9.8m/s2
We need to calculate final velocity, vf = ?
a= (vf-vi )/t
vf = vi+ at
Final velocity, vf = 10m/s.
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