⚛️Physics

Kinematics

Study of motion — displacement, velocity, acceleration, equations of motion, projectile motion and relative motion.

Class 11Class 12

What You Will Learn in Kinematics

Kinematics is the branch of mechanics that studies motion — displacement, velocity, and acceleration — without considering the forces causing it.

Displacement (vector) vs Distance (scalar); Velocity = Δs/Δt; Acceleration = Δv/Δt.
Equations of motion (uniform acceleration): v=u+at; s=ut+½at²; v²=u²+2as; s=½(u+v)t.
Projectile motion: horizontal component uniform (aₓ=0), vertical under gravity (ay=-g).
Range R = u²sin2θ/g; Max height H = u²sin²θ/2g; Time of flight T = 2usinθ/g.
Relative velocity: velocity of A relative to B = vA - vB.
For free fall: a=-g; using v²=u²-2gh, v=√(2gh) on reaching ground from height h.

Key Formulas

v=u+ats=ut+½at²v²=u²+2asR=u²sin2θ/gH=u²sin²θ/2gT=2usinθ/g

Example

A ball thrown horizontally at 20 m/s from a 45 m cliff hits ground after t=√(2×45/10) = 3 s.

Solved Numerical Example

Projectile problem: A ball is projected at 60° with u=20 m/s. Find R, H, T. (g=10)
R = (20²×sin120°)/10 = (400×√3/2)/10 = 34.64 m
H = (20²×sin²60°)/(2×10) = (400×0.75)/20 = 15 m
T = (2×20×sin60°)/10 = (40×√3/2)/10 = 3.46 s

Expected Exam Questions — Kinematics

Q1.A car starts from rest and accelerates at 5 m/s² for 10 s. Find distance covered.

Answer: u=0, a=5 m/s², t=10 s. s = ut + ½at² = 0 + ½×5×100 = 250 m.

Q2.What is the angle of projection for maximum range of a projectile?

Answer: R = u²sin2θ/g. Maximum when sin2θ=1, i.e., 2θ=90°, so θ=45°. Maximum range = u²/g.

Q3.Distinguish between distance and displacement.

Answer: Distance: total path length, scalar, always ≥ 0. Displacement: shortest straight-line from initial to final position, vector, can be negative. Example: running one lap of a 400m track — distance=400m, displacement=0.

Q4.A stone is dropped from 80 m height. Find time to reach ground. (g=10 m/s²)

Answer: u=0, a=g=10, s=80. s=ut+½gt² → 80=½×10×t² → t²=16 → t=4 s.

🔘 MCQ Practice — Kinematics

MCQ 1.A body is in uniform circular motion. Its acceleration is:

A. Zero

B. Directed tangentially

C. Directed towards centre ✓

D. Directed away from centre

✓ Correct Answer: Directed towards centre

MCQ 2.The area under a velocity-time graph represents:

A. Acceleration

B. Force

C. Displacement ✓

D. Speed

✓ Correct Answer: Displacement

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Frequently Asked Questions — Kinematics

What is Kinematics in Physics?

Kinematics is the branch of mechanics that studies motion — displacement, velocity, and acceleration — without considering the forces causing it.

A car starts from rest and accelerates at 5 m/s² for 10 s. Find distance covered.

u=0, a=5 m/s², t=10 s. s = ut + ½at² = 0 + ½×5×100 = 250 m.

What is the angle of projection for maximum range of a projectile?

R = u²sin2θ/g. Maximum when sin2θ=1, i.e., 2θ=90°, so θ=45°. Maximum range = u²/g.

Distinguish between distance and displacement.

Distance: total path length, scalar, always ≥ 0. Displacement: shortest straight-line from initial to final position, vector, can be negative. Example: running one lap of a 400m track — distance=400m, displacement=0.

A stone is dropped from 80 m height. Find time to reach ground. (g=10 m/s²)

u=0, a=g=10, s=80. s=ut+½gt² → 80=½×10×t² → t²=16 → t=4 s.

How do I prepare Kinematics for exams?

To master Kinematics, start by reading the theory carefully, then go through solved examples step by step. Practice numericals (if applicable), revise key formulas, and attempt previous year questions. SII notes cover all these aspects in a structured manner.

Are these Kinematics notes free?

Yes! SII provides free access to Kinematics notes and introductory study materials. Enrolled students get full access to detailed notes, solved papers, and live doubt-clearing sessions.

Which exams ask questions from Kinematics?

Kinematics is an important topic tested in Class 11, Class 12 board exams, as well as JEE Main, JEE Advanced, NEET. It frequently appears in both short-answer and long-answer sections.