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Uniformly Acceleration Motion: When describing a state of increasing speed, the word acceleration is often used in everyday English. Acceleration occurs when the velocity of an object changes: either increasing speed (what people usually mean when they say acceleration), decreasing speed (also called deceleration or retardation), or changing direction (called centripetal acceleration). That’s right; even when an object does not speed up or slow down, a change in direction results in acceleration. An acceleration effect is a function of velocity change, and velocity is a vector quantity with magnitude and direction. An apple falling to the ground accelerates, a car stopping at a traffic light accelerates, and the moon in orbit around the Earth accelerates. Whenever an object’s speed changes, or its direction changes, it is said to be accelerating.
Uniformly Acceleration Motion
According to this definition, uniform acceleration refers to the acceleration of an object regardless of time. Uniformly accelerated motion occurs when a number equal to acceleration in a motion does not change as a function of time. Some uniformly accelerated motion examples include a ball rolling downhill, a skydiver jumping from an airplane, a ball dropped from the top of a ladder, and a bicycle with its brakes applied. It is important to note that these examples of uniform application do not maintain absolute uniformity of acceleration due to the interference of gravity and/or friction. Nevertheless, these are still some of the cases where acceleration would be uniform if gravitational force and friction were zero.
Calculate acceleration by dividing velocity by time or by dividing meters per second [m/s] by seconds [s]. Distance divided by time twice is the same as distance divided by the square of time. Therefore, the SI unit of acceleration is the meter per second squared.
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Uniform Acceleration Equations
When motion is in a straight line with constant acceleration, there are three equations of motion that are helpful in determining one of the unknown parameters:
v = u + at
X = ut + ½ at2
v2= u2 + 2as
v = final velocity of the particle
u = initial velocity of the particle
s = displacement of the particle
a = acceleration of the particle
t = the period of time the particle is considered
It is important to maintain the sign convention when applying these equations. One direction should be considered positive and the other negative.
Freely falling bodies are a common example of uniformly accelerated motion. The only acceleration that acts on the body is gravity’s acceleration (g). Considering the upward direction as the positive, gravity’s acceleration (g) will be negative since it is in a downward direction.
Uniformly accelerated motion in a plane
A projectile is one of the most popular examples of motion in a plane with uniform acceleration. During a projectile motion, the only acceleration acting on the particle is the acceleration due to gravity (g). In level heading – or the speed in x-course will be consistent since there is no speed increase. Accordingly, we can apply the conditions of movement independently in two headings to get results.
As a rule, a consistently sped-up movement is the one where the speed increase of the molecule all through the movement is uniform. It very well may be moved in one aspect, two aspects, or three aspects.
Derivation of equations of motion by the algebraic method
Derivation of 1st Equation of Motion:
It is well known that the acceleration of a body is defined as the rate at which velocity changes.
Mathematically, acceleration is represented as follows:
a = v-u/t
V represents the final velocity, and U represents the initial velocity.
Rearranging the above equations, we arrive at the first equation of motion as follows
v= u+at
Derivation of 2nd Equation of Motion
Velocity is defined as the rate of change of displacement. This is mathematically represented as:
Velocity = Displacement / Time
Rearranging above we get
Displacement = Velocity ✕ Time
It is possible to substitute average velocity for velocity in the equation above if the velocity is not constant:
Displacement =[ (Initial Velocity + Final Velocity) / 2] ×Time
Substituting the above equations with the notations used in the derivation of the first equation of motion, we get
s = (u + v) / 2 × t
In terms of the first equation of motion, we can see that v = u + at. Putting this value of v in the above equation, we get
s= u + (u+at)/2 × t
This can be written as;
s= 2u+ at/2 ×t
s= (u+½ at )×t
On further simplification, the equation becomes:
s=ut + ½ at2
Derivation of 3rd Equation of Motion
We know that displacement is the rate of change of position of an object. Mathematically, this can be represented as:
Displacement = (Initial velocity + Final Velocity)/2 * t
The above equation becomes the following when using the standard notation
s= (u+v) /2 × t
From the first equation of motion, we know that
v=u+at
Rearranging the above formula, we get
t=v-u/a
Substituting the value of t in the displacement formula, we get
s= (v+u)/2 × (v-u)/a
s=(v2-u2)/2a
2as= v2-u2
Rearranging we get,
v2=u2+2as
Weightage of uniformly acceleration motion in competitive exams (JEE and NEET)
On analyzing the previous year’s exam papers, it is observed that, on average, one to two questions are asked every year. Here is some data based on previous examinations to support the above argument.
The investigation of movement by Galileo Galilei (1564-1642) in the late sixteenth and mid-seventeenth hundreds of years and by Sir Isaac Newton during the seventeenth century is a foundation of present-day Western test science. For nearly 20 years, Galileo meticulously coordinated the movements of articles moving down smooth slopes. He found that the distance an article headed out was relative to the square of the time that it was moving. From these tests came the main right idea of sped-up movement. Newton needed to know what the personality of speed increase was, yet in addition to why it happened by any stretch of the imagination.
JEE Mains Physics Chapter Wise Weightage
2021
| Chapter | Questions |
| Laws Of Motion | 1 |
2020
| Chapter | Question |
| Laws Of Motion | 2 |
2019
| Chapter | Question |
| Circular Motion | 1 |
2018
| Chapter | Questions |
| Circular Motion | 1 |
