JEE Physics – Kinematics

Physics – Chapter 2: Kinematics (JEE)

1. What is Kinematics?

Kinematics is the branch of physics that deals with the **description of motion** without considering the forces causing the motion.

Kinematics answers **how an object moves**, not **why it moves**.

2. Rest and Motion

An object is said to be at rest or in motion **relative to a reference frame**.

There is no absolute rest or absolute motion.

3. Point Object

An object is treated as a point object when its size is negligible compared to the distance travelled.

4. Scalar and Vector Quantities

Scalar	Vector
Magnitude only	Magnitude + direction
Distance, Speed	Displacement, Velocity

5. Distance and Displacement

Distance: Total path length (scalar)
Displacement: Shortest distance from initial to final position (vector)

Magnitude of displacement ≤ distance

6. Speed

Speed = $\dfrac{\text{Distance}}{\text{Time}}$

Average speed
Instantaneous speed

7. Velocity

Velocity = $\dfrac{\text{Displacement}}{\text{Time}}$

Velocity can be positive, negative, or zero.

8. Acceleration

Acceleration = $\dfrac{\Delta \text{Velocity}}{\Delta \text{Time}}$

Uniform acceleration
Non-uniform acceleration

9. Equations of Motion (Uniform Acceleration)

$v = u + at$

$s = ut + \dfrac{1}{2}at^2$

$v^2 = u^2 + 2as$

10. Graphical Representation of Motion

Graph	Slope / Area Meaning
Position–Time	Slope = Velocity
Velocity–Time	Slope = Acceleration
Velocity–Time	Area = Displacement

11. Motion Under Gravity

Acceleration due to gravity:

$g = 9.8\ \text{m/s}^2$

For upward motion, take $a = -g$

12. Free Fall

Motion under gravity only, no other force acting.

$v = gt,\quad s = \dfrac{1}{2}gt^2$

13. Relative Velocity

$\vec{v}_{A/B} = \vec{v}_A - \vec{v}_B$

Very important for river-boat and train problems.

14. Motion in One Dimension

Motion along a straight line (x-axis or y-axis).

15. Motion in Two Dimensions

Motion in a plane, resolved into x and y components.

16. Projectile Motion

Time of flight: $T = \dfrac{2u\sin\theta}{g}$

Range: $R = \dfrac{u^2\sin2\theta}{g}$

Maximum height: $H = \dfrac{u^2\sin^2\theta}{2g}$

17. Horizontal Projectile

Initial velocity has only horizontal component.

18. Special Cases of Projectile

Maximum range at $45^\circ$
Complementary angles give same range

19. Common JEE Mistakes

Mixing distance and displacement
Wrong sign of acceleration
Forgetting vector nature of velocity
Incorrect graph interpretation

20. Final Revision Checklist

You have mastered Kinematics if you can:

Apply equations correctly
Interpret graphs accurately
Solve projectile motion confidently
Handle relative velocity problems