Content Writer
Acceleration is the rate at which an object changes its velocity. An object is said to be in acceleration if there is a change in its velocity. The change in the velocity can either be an increase or decrease in the speed of an object or a change in the direction of motion.
Acceleration is equal to the difference between the initial and final velocities divided by the time. Some examples of acceleration include the moon orbiting around the earth, the falling of an apple, etc. An object is said to be accelerating if it is changing its velocity time and again.
Read More: NCERT Solutions for Cass 11 Physics Motion in a Plane
Key Terms: Acceleration, Acceleration Formula, Velocity, Uniform Acceleration, Instantaneous Acceleration, Average Acceleration, Non-Uniform Acceleration
What is Acceleration?
[Click Here for Sample Questions]
Acceleration is defined as the rate of change of velocity with respect to time in terms of both speed and direction.
- Acceleration is denoted by the symbol ‘a’ and the SI unit of acceleration is m/s2.
- It is a vector quantity since it has both direction and magnitude.
- Acceleration is the second derivative of position with respect to time.
- It is the first derivative of velocity with respect to time.
Acceleration
Acceleration Formula
[Click Here for Previous Years' Questions]
Acceleration is the rate of change of the velocity of an object. The change in velocity is defined as, (v – u) where v and u are the final and the initial velocities.
Thus, the acceleration of an object is given by,
Acceleration = Change in Velocity / Time taken
Mathematically, the acceleration formula is given as:
a = (v – u) / t
Where
- a is the acceleration (in m/s2)
- v is the final velocity (in m/s)
- u is the initial velocity (in m/s)
- t is the time interval (in seconds)
Read More: Angular Acceleration Formula
Solved ExampleExample: A truck accelerates from 6 m/s to 10 m/s in a time period of 10 s. What will be its acceleration? Solution: According to the question,
Using the Acceleration Formula, Acceleration a = (v – u) / t a = (10 m/s – 6 m/s) / 10 s a = 0.4 m/s2 Thus, the acceleration of the truck is calculated as 0.4 m/s2. |
Positive, Negative and Zero Acceleration
Acceleration can be positive, negative or zero.
- When an object’s velocity increases with time, it can be termed Positive Acceleration.
- When an object’s velocity decreases with time, it can be termed Negative Acceleration or Retardation.
- When the velocity is zero, it is termed Zero Acceleration.
Read More: Differences between Acceleration and Velocity
Types of Acceleration
[Click Here for Previous Years' Questions]
The different types of acceleration associated with an object are classified below:
Uniform and Non-Uniform Acceleration
- If an equal amount of velocity increases in equal intervals of time, then the object is said to be in uniform acceleration.
- If the velocity of the object changes by unequal amounts in equal intervals of time, the object is said to be non-uniform acceleration.
Average Acceleration
Average Acceleration is the change in velocity for a particular specified time interval. It is the total change in velocity in the given interval divided by the total time taken for the change. Average acceleration can be calculated as
av = Δ v / Δ t
av = (vf – vi) / (tf – ti)
Where
- vf is the final velocity.
- vi is the initial velocity.
- ti is the initial time.
- tf is the final time.
Read More: Average Acceleration Formula
Instantaneous Acceleration
- Instantaneous acceleration is the ratio of change in velocity during a given time interval such that the time interval goes to zero.
- To calculate instantaneous acceleration, the average velocity is calculated between two points in time separated by Δt and let Δt approach zero.
Read More: Motion in a Plane Important Questions
Velocity-Time Graph for Acceleration
[Click Here for Sample Questions]
In the velocity-time graph, time is plotted along the x-axis and velocity is plotted along the y-axis. Here are a few velocity-time graphs for acceleration:
(I) When acceleration is zero or the velocity of the object is constant.
V-T Graph when Acceleration is Zero
(II) When Acceleration decreases and increases.
V-T Graph when Acceleration Decreases or Increases
(III) When the object is moving with uniform acceleration and its initial velocity is zero.
Constant Acceleration
Read More: Acceleration Time Graph
(IV) When the particle is moving with constant retardation (negative acceleration).
Constant Retardation
(V) When the object moves with non-uniform acceleration and its initial velocity is zero.
Things to Remember
- Acceleration is defined as the rate of change of velocity with respect to time.
- In acceleration, the change in the velocity could be an increase or decrease in speed or a change in the direction of motion.
- Acceleration is a vector quantity and the SI unit of acceleration is m/s2.
- Acceleration is the change in velocity divided by the time taken which can be expressed as a = (v – u) / t.
- If the velocity increases, decreases or is zero with respect to time, then the acceleration is termed as positive, negative and zero acceleration respectively.
- Acceleration can be classified into various types namely uniform and non-uniform motion, average acceleration and instantaneous acceleration.
Previous Years’ Questions (PYQs)
- The displacement, velocity and acceleration in a simple harmonic motion… (JKCET 2013)
- The dimensional formula for acceleration, velocity and length…
- Average acceleration vector for a particle having uniform circular motion…
- The effective acceleration of a body, when thrown upwards with acceleration…
- A particle starts from rest. Its acceleration (a) versus time (t)... (JEE Advanced 2004)
- The depth d at which the value of acceleration due to gravity becomes… (KEAM)
- What happens to the acceleration due to gravity with the… (JKCET 2014)
- The acceleration of a moving body is found from the… (KEAM)
- The acceleration of any electron due to the… (BCECE 2010)
- The ratio of magnitudes of average velocity to average speed…
Sample Questions
Ques. What is the difference between acceleration and velocity? (3 Marks)
Ans. The major differences between acceleration and velocity are as follows:
| Acceleration | Velocity |
|---|---|
| Acceleration is the change in the velocity of an object with respect to time. | Velocity is the speed of an object in a particular direction. |
| Acceleration is calculated as Velocity/Time | Velocity is calculated as Displacement/Time. |
| Its SI unit is m/s2. | Its SI unit is m/s. |
Ques. What will be the final velocity of the ball dropped from the fourth floor, if the ball takes 18 seconds before hitting the ground? The acceleration due to gravity is given as g = 9.80 m/s2. (3 Marks)
Ans. According to the question,
- Initial velocity (vi) = 0 m/s
- Final velocity, (vf) =?
- Acceleration due to Gravity (a) = g = 9.80 m/s2
- Time (t) = 18 s
Acceleration is calculated as:
a = (vf−vi)t
vf = vi + at
vf = 0+(9.80×18)=176.4 m/s
Thus, the final velocity of the ball will be 176.4 m/s.
Ques. Calculate the acceleration of an object that moves with a uniform velocity. (3 Marks)
Ans. Since the velocity is uniform, the initial and final velocities are equal and are given as V.
Acceleration is calculated as
a = (vf −vi)/t
a = 0/t
∴ a = 0
Thus, the acceleration of an object that moves with a uniform velocity is zero.
Ques. A truck is moving with a constant velocity of 5 m/s. He stops the truck for some time and then accelerates forward. After 20 seconds, the driver stops accelerating and maintains a constant velocity of 25 m/s. Calculate the acceleration of the truck. (3 Marks)
Ans. According to the question,
- Initial velocity (vi) = 5 m/s
- Final velocity (vf) = 25 m/s
- Time (t) = 20 s
Acceleration is calculated as
a=(vf−vi)t
a = (25−5)/20
∴ a = 1 m/s2
Thus, the acceleration of the truck is 1 m/s2.
Ques. A man is driving a car at 108 km/h and slows down to bring it to 72 km/h in 5 s. What will be the retardation of the car? (3 Marks)
Ans. As per question,
- Initial velocity (u) = 108 km/h = 30 m/s.
- Final velocity (v) = 72 km/h = 20 m/s
- Time taken (t) = 5 seconds
Acceleration is calculated as
a = (v-u)/t
a = (20-30)/5
a = -10/5 = -2 m/s2
Thus, the retardation of the car is -2 m/s2.
Ques. A car moves from rest and then accelerates uniformly at the rate of 7.5 m/s2 for 10 s. What will be the velocity of the car? (3 Marks)
Ans. Given parameters are
- Initial velocity (u) = 0, since the car was at rest.
- Acceleration (a) = 7.5 m/s2
- Time (t) = 10 s
Using the acceleration formula,
a = (v-u)/t
v = u + at
v = 0 + 7.5 × 10 = 75 m/s.
The velocity of the car is 75 m/s.
Ques. What do you mean by centripetal acceleration and Coriolis acceleration? (3 Marks)
Ans. Centripetal acceleration is when an object is moving in a circle and its acceleration vector is pointed towards the centre of that circle. The SI unit of centripetal acceleration is also m/s2.
Coriolis acceleration is caused due to the rotation of the earth and is experienced by the particles that move along the surface of the earth.
Ques. A car is stationary and then it takes 5 seconds to reach a speed of 16m/s. What will be its acceleration? (3 Marks)
Ans. As per the question,
- Initial velocity (u) = 0 (As the object is at rest.)
- Final velocity (v) = 16 m/s
- Time taken (t) = 5 seconds
Acceleration is calculated as
a = (v-u)/t
a = (16-0)/5
a = 16/5 = 3.2 m/s2
Thus, the acceleration of the car is 3.2 m/s2.
Ques. What is acceleration? (3 Marks)
Ans. Acceleration refers to the rate at which an object changes its velocity. It can either be an increase or decrease in the speed of an object or a change in the direction of motion. Acceleration refers to the difference between the initial and final velocities divided by the time.
Ques. Give some examples of acceleration. (3 Marks)
Ans. Here are a few examples of acceleration:
- An car moving north at 10 meters per second
- An apple falling down from a tree.
- Ritika walks east at 3 kilometers per hour.
- Acceleration due to gravity.
- A ball falling down from a balcony.
Ques. What factors affect acceleration? (3 Marks)
Ans. Acceleration is affected by two factors:
- Mass of the object.
- Amount of force applied to the object.
The acceleration of an object increases with increased force and decreases with increased mass. Thus, it is affected by these two factors.
Ques. Can acceleration be negative? (2 Marks)
Ans. Yes, acceleration can be negative. When an object is slowing down, the acceleration is in the opposite direction as the velocity, thus, this object has a negative acceleration. Negative acceleration is also referred to as retardation.
Check-Out:
Comments