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JEE Main Kinematics Revision Notes

## JEE Main Kinematics Revision Notes - PDF Download

Today, we will discuss the notes of kinematics for the reference of many JEE Main aspirants. Inertial reference frames or inertial frames hold the concept of Newtonian mechanics. The average speed or average velocity can be written as Vav.

The mathematical expression is: Vav = Δr / Δt

Also, the instantaneous speed can be expressed as

\[\nu\] = \[\lim_{\triangle t\to 0}\] \[\frac{\triangle s}{\triangle t}\] = \[\frac{ds}{dt}\]

And, \[\overrightarrow{\nu}\] = \[\lim_{\triangle t\to 0}\] \[\frac{\triangle \overrightarrow{r}}{\triangle t}\] = \[\frac{d \overrightarrow{r}}{d t}\]

### Note:

1. There is an alteration in velocity when we alter the speed or the direction of the object.

2. We can conclude the velocity of a particle as zero when it completes its one revolution in a circular path.

3. Possessing the zero speed is totally impossible with a non-zero velocity.

When it comes to average acceleration, it can be written as

\[\overrightarrow{a}\]_{a𝜈} = \[\frac{\triangle \overrightarrow{\nu}}{\triangle t}\]

The expression over a time interval Δt

We can write the instantaneous acceleration of a particle where the velocity is changing at that instant of time.

\[\overrightarrow{a}\]_{a𝜈} = \[\lim_{\triangle t\to 0}\] \[\frac{\triangle \overrightarrow{\nu}}{\triangle t}\] = \[\frac{d \nu}{dt}\]

### Kinematics Notes for IIT JEE

We have enlisted the three equations of motion for a body with uniform acceleration written below.

V = u + at

s = ut + 1/2 at2

v2 = u2+ 2as

In the above equations, these are the symbols used

u = initial velocity

v = final velocity

a = acceleration

s = displacement traveled by the body

t = time

Note: When a body accelerates, the value of acceleration id ‘+ve’, and when it deaccelerates, it is ‘- ve’.

For the displacement of the body in the nth second can be written as

sn= u + a/2 (2n-1)

### Kinematics JEE Mains Notes

We have mentioned the equation of motion in an inclined plane.

(Image to be added soon)

i. For The Perpendicular Vector

When a body is at the top, these values are

t = 0

u = 0

and a =g sin θ

Equation of motion can also be written as,

(g sin θ) t = v

½ (g sin θ) t2= s

2 (g sin θ) s = v2

ii. Total Time Required to Reach at the Bottom by the Body = T, Then

s = ½ (g sin θ) t2

t = √ (2s/g sin θ)

But,

sin θ = h / s

or s= h / sin θ

So, t = (1/ sin θ) √ (2h / g)

at the bottom, the body’s velocity can be written as

g (sin θ) t = v = √2gh

Change of mass

The relativistic mass (M) of a body per Einstein’s mass-variation formula can be written as,

m0 ÷ √ (1 - v2 / c2) = M

Where,

m0 = rest mass of the body

v = speed of the body

c = speed of light.

### Kinematics revision notes

There are some solved kinematics examples given below.

Q1. A Spacecraft Accelerates Down the Runway at 4.20 m/s2 for the Time 28.6 Sec Until it Lifts Off the Ground. What Will Be the Distance Travelled Before Departure?

Ans: Given data

t = 28.6 sec

a = 4.20 m/s2

The formula states that

Distance (d) = vi * t + 0.5 * a * t2

d = (0 m/s) * (28.6 s) + 0.5*(4.20 m/s2) *(28.6 s)2

d = 1717.72 m

Q2. A Player Tossed a Ball Upward and it Stays up to 9 s. Then, Calculate the Total Altitude Gained by the Ball Before it Reaches Its Highest.

Ans: We know that the time required to attain the topmost point is half of the total hang-time.

So, the time = - 4.5 s

We need to use: vf = vi + a * t

0 m/s = vi + (- 9.8 m/s2) * (4.5 s)

vi = 44.1 m/s

Again, we must use: vf2 = vi2 + 2 * a * d

(0 m/s)2 = (44.1 m/s)2 + 2*(-9.8 m/s2) * d

0 m2/s2 = (1944.8 m2/s2) + (-19.6 m/s2) * d

(19.6 m/s2) * d = 1944.8 m2/s2

d = (1944.8 m2/s2) / (19.6 m/s2)

d = 99.2 m

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### Kinematics PYQP

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In the chapter’s PDF, it contains numerical problems which are answered precisely by explaining each question.

The answers are explained for the respective questions which are quite understandable as per a student’s point of view.

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1. What Do You Mean by the Kinematics of a Rigid Body?

A kinematic rigid body can be defined as a specific way to move a rigid body instead of moving the other objects without any intention. An example can be written about controlling an elevator with a script via its transform property, instead of displacing other objects.

2. What Are Some of the Kinematics Usages in Real-Life?

There are many real-life usages of kinematics such as;

Kinematics is used in machine components to govern the unknown speed of an object, which is linked with another object moving at a known speed.

We can calculate the linear velocity of a piston linked with a flywheel, which is rotating at a known speed.

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