Kinematics – Study Notes (TS EAMCET Physics)
Kinematics is the branch of mechanics that deals with motion without considering the causes (forces).
In EAMCET you’ll encounter problems on displacement, velocity, acceleration, and the basic equations of motion (often referred to as the “SUVAT” equations).
1. Simple Explanation
| Concept | What is it? | Key Symbol(s) | Unit |
|---|---|---|---|
| Displacement (𝑠) | Net change in position (vector). | 𝑠 | m |
| Velocity (𝑣) | Rate of change of displacement (vector). | 𝑣 | m s⁻¹ |
| Speed | Magnitude of velocity (scalar). | 𝑣 | m s⁻¹ |
| Acceleration (𝑎) | Rate of change of velocity (vector). | 𝑎 | m s⁻² |
| Time (𝑡) | Duration of motion. | 𝑡 | s |
Important: In all EAMCET questions the SI system is used unless otherwise specified.
2. Key Points & Formulas
2.1 Uniform (Constant) Motion
- Velocity is constant → Acceleration = 0.
- Displacement:
s = v * t - Average velocity:
v_avg = (v_initial + v_final) / 2
2.2 Uniformly Accelerated Motion (UAM)
- Acceleration is constant.
- SUVAT (Seven) equations – only the following four are needed for most EAMCET problems:
| Equation | When to use | Variables |
|---|---|---|
v = u + a t |
Final velocity known | u = initial velocity |
s = u t + ½ a t² |
Distance travelled | |
v² = u² + 2 a s |
No time needed | |
s = ½ (u + v) t |
Average velocity approach |
Notation:
u – initial velocity, v – final velocity, s – displacement, a – acceleration, t – time.
2.3 Projectile Motion (2‑D)
-
Horizontal component:
vₓ = v₀ cosθ(constant)
x = vₓ t -
Vertical component:
vᵧ = v₀ sinθ – g t
y = v₀ sinθ t – ½ g t² -
Range (on level ground):
R = (v₀² sin 2θ) / g -
Maximum height:
H = (v₀² sin²θ) / (2 g) -
Time of flight:
T = (2 v₀ sinθ) / g
2.4 Circular Motion (if covered)
- Angular displacement:
θ = ω t - Linear speed:
v = r ω - Centripetal acceleration:
a_c = v² / r = ω² r
3. Worked Example (EAMCET‑style)
Question:
A car starts from rest and accelerates uniformly at 2.0 m s⁻².
(a) Find the time taken to cover a distance of 100 m.
(b) What is its final speed at that instant?
Solution
Given:
u = 0
a = 2.0 m s⁻²
s = 100 m
(a) Time (t)
Use s = u t + ½ a t²
100 = 0 * t + ½ * 2.0 * t²
100 = 1.0 * t²
t² = 100 → t = 10 s (positive root)
(b) Final velocity (v)
Use v = u + a t
v = 0 + 2.0 * 10 = 20 m s⁻¹
Answer:
(a) t = 10 s
(b) v = 20 m s⁻¹
Tip: Always check the units; they should cancel out to give a meaningful result.
4. Quick Revision Summary
| Topic | Formula(s) | Typical EAMCET Question Type |
|---|---|---|
| Displacement | s = v t |
Multiple‑choice (vector vs scalar) |
| Constant velocity | v = Δs/Δt |
Numerical (time, distance, speed) |
| Constant acceleration | v = u + a ts = u t + ½ a t²v² = u² + 2 a s |
Numerical (find missing variable) |
| Projectile motion | R = v₀² sin 2θ / gH = v₀² sin²θ / (2 g) |
Numerical (range, height, time) |
| Circular motion | v = r ωa_c = v²/r |
Numerical (centripetal acceleration) |
Quick Tips
-
Identify the knowns and unknowns.
Pick the equation that contains the unknown you need to find and the knowns you have. -
Check the sign of acceleration.
Positive for speeding up, negative (deceleration) if slowing down. -
Remember g = 9.8 m s⁻² (often approximated to 10 m s⁻² for quick mental maths).
-
Use vector–scalar distinction.
Speed is scalar; velocity is vector. In many EAMCET questions, they ask for magnitude only, but be careful with directions in projectile problems. -
Practice unit analysis – it helps catch errors instantly.
Final Thought
Mastering the SUVAT equations and knowing how to decide which one to use will