General Q&A for Class 12 · Page 181
5,215 free answers in General for Class 12 students, across CBSE, ICSE and State boards.
Question & Answer
Questions
- GeneralClass 12All
What is the formula for work?
Work is calculated using the formula W = F × d × cos(θ), where W represents work, F is the applied force, d is the displacement, and θ is the angle between the force and displacement vectors. When force and displacement are in the same direction, this simplifies to W = F × d. Work measures the energy transferred when a force moves an object through a distance.
- GeneralClass 12All
Why do we sometimes use P = I²R instead of P = E × I?
Both formulas are valid—they serve different analytical purposes: P = E × I (or P = V × I): Shows total power in the circuit Easy when voltage and current are known Best for calculating consumed power Used for overall circuit analysis P = I²R: Shows power dissipated as heat in a resistor Highlights how current affects power los
- GeneralClass 12All
What formula should I use to find power from voltage, current, and resistance?
When you have all three values, you can use any formula but verify your data first: Primary formulas: P = V × I P = I² × R P = V² / R Verification check: Use Ohm's Law (V = I × R) to ensure your values are consistent. Best practice: Calculate using two different formulas Compare results they should match</li
- GeneralClass 12All
How do I calculate power loss in electrical wiring?
Power loss in wires is primarily due to resistance heating, calculated using: Power Loss = I² × R Where: I = current flowing through the wire (A) R = resistance of the wire (Ω) To find wire resistance: R = ρ × (L / A) ρ = resistivity of material (copper: 1.68 × 10⁻⁸ Ω·m) L = length of wire (m) A = cross-sectional area (
- GeneralClass 12All
What are common mistakes when calculating power in complex systems?
Top mistakes to avoid: Unit inconsistency Mixing watts and kilowatts Using degrees instead of radians for angular velocity Forgetting to convert RPM to rad/s Ignoring efficiency Assuming 100% energy conversion Not accounting for friction, heat loss Reality: motors are 80-95% efficient Using instantaneous vs. ave
- GeneralClass 12All
What is the formula for escape velocity?
Escape velocity is calculated using: v_escape = √(2GM/r) where G is the gravitational constant (6.674 × 10⁻¹¹ N·m²/kg²), M is the mass of the planet, and r is the distance from the center of the planet. For Earth specifically: Escape velocity ≈ 11.2 km/s or about 40,270 km/h This is the minimum speed needed to break free from Earth's gravity Direction doesn't matter—i
- GeneralClass 12All
In which situations should we use the formula (u+v)/2 for average velocity?
Use this formula ONLY when acceleration is constant throughout the motion. When to use it: Uniformly accelerated motion (constant a) Linear velocity-time graphs Motion under constant force When NOT to use it: Variable acceleration Circular motion (even at constant speed) Non-linear velocity changes Example: A car accelerates uniformly
- GeneralClass 12All
How do you find final velocity from acceleration and distance?
Use the equation: v² = u² + 2as which rearranges to: v = √(u² + 2as) If starting from rest (u = 0), this simplifies to: v = √(2as) This equation is perfect when you: Know the distance traveled (s) Know the acceleration (a) Don't know or need the time (t) Example: A car accelerating at 2 m/s² from rest over 100 meters reaches v = &
- GeneralClass 12All
What is the formula for velocity in science?
The basic velocity formula in science is: v = d/t where v represents velocity, d is displacement (distance traveled in a specific direction), and t is time. Points to understand: Velocity is a vector quantity, meaning it has both magnitude (speed) and direction Common units include meters per second (m/s), kilometers per hour (km/h), and miles per hour (mph) Displacem
- GeneralClass 12All
How is average velocity calculated?
Average velocity is calculated using: v_avg = (total displacement) / (total time) Or when you know initial and final velocities: v_avg = (u + v) / 2 (Note: The second formula only works for constant acceleration) Important distinctions: The (u + v)/2 formula ONLY works when acceleration is constant throughout the motion For non-uniform acceleration, use total displacement divided by total time Average
- GeneralClass 12All
How do you calculate instantaneous velocity?
Instantaneous velocity is the velocity at a specific moment in time. Mathematically: v = lim(Δt→0) Δx/Δt or v = dx/dt (the derivative of position with respect to time) Practical approaches: For constant acceleration: v = u + at (where u is initial velocity, a is acceleration, t is time) From a velocity-time graph: the y-value at any point gives instantaneous velocity
- GeneralClass 12All
How do you find velocity when you know height?
For objects in free fall or projectile motion, use: v = √(2gh) where g is gravitational acceleration (9.8 m/s²) and h is height. This gives the velocity just before impact. Step-by-step calculation: Multiply height by 2: 2 × h Multiply result by g (9.8 m/s²) Take the square root of the result Example: A ball dropped from 20 meters has final velocity = √(2 &t
- GeneralClass 12All
How do you calculate velocity from force and distance?
You cannot directly calculate velocity from only force and distance. However, if you also know mass, use the work-energy theorem: v = √(2Fd/m) where F is force, d is distance, and m is mass. The physics behind it: Work done by force = F × d This work converts to kinetic energy = ½mv² Setting them equal: Fd = ½mv², then solve for v
- GeneralClass 12All
How do you find velocity from kinetic energy and mass?
Use the kinetic energy formula rearranged: v = √(2KE/m) where KE is kinetic energy in joules and m is mass in kilograms. Quick calculation method: Multiply kinetic energy by 2 Divide by mass Take the square root Example: A 5 kg object with 250 J kinetic energy has velocity = √(2 × 250 / 5) = √100 = 10 m/s.
- GeneralClass 12All
How do you calculate velocity from momentum?
Use the momentum formula rearranged: v = p/m where p is momentum (in kg·m/s) and m is mass (in kg). This is one of the simplest velocity calculations. Remember: Momentum = mass × velocity, so velocity = momentum ÷ mass Both momentum and velocity are vectors (have direction) Units must be consistent: if p is in kg·m/s and m in kg, v will be in m/s Example: A 6
- GeneralClass 12All
How to calculate velocity when force and time are given?
If you know force, time, and mass, use Newton's second law combined with kinematics: v = (F/m) × t + u where F is force, m is mass, t is time, and u is initial velocity (0 if starting from rest). Understanding the formula: F/m gives you acceleration (from F = ma) Then use v = u + at If starting from rest, v = (F/m) × t <str
- GeneralClass 12All
How to calculate power when mass, velocity and time are given?
Power is the rate of doing work. With mass and velocity, first find kinetic energy, then divide by time: P = KE/t = (½mv²)/t where m is mass, v is velocity, and t is time. Example: A 100 kg object reaches 20 m/s in 10 seconds. Power = (½ × 100 × 20²) / 10 = 20,000 / 10 = 2,000 watts.
- GeneralClass 12All
What are all the formulas relating velocity and acceleration?
The main equations of motion (kinematic equations) for constant acceleration are: v = u + at (final velocity from initial velocity and acceleration) s = ut + ½at² (displacement from velocity and acceleration) v² = u² + 2as (final velocity without time) s = ½(u + v)t (displacement from average velocity) Where: v = final velocity, u = initial velocity, a = acceleration, t = time
- GeneralClass 12All
Is v = ½at² a correct velocity formula?
No, this is incorrect! The correct formula is: v = at (when starting from rest) or the general case: v = u + at The formula s = ½at² gives displacement, not velocity. Common confusion: s = ½at² → displacement formula (distance traveled) v = at → velocity formula (when u = 0) The ½ factor appears in displacement because velocity increases
- GeneralClass 12All
. How is power calculated in combined mechanical and electrical systems?
Electromechanical systems (motors, generators) involve energy conversion between electrical and mechanical forms: For Electric Motors: Electrical Input Power: P_in = V × I × cos(φ) cos(φ) = power factor (for AC systems) Mechanical Output Power: P_out = τ × ω Efficiency: η = (P_out / P_in) × 100% <stron