Kcse Physics 594477

1. State the problem: Calculate the speed of a car that travels 100 meters in 5 seconds. 2. Formula: Speed $v = \frac{d}{t}$ where $d$ is distance and $t$ is time. 3. Calculation: $v = \frac{100}{5} = 20$ m/s. 4. Explanation: Speed is distance divided by time. --- 1. State the problem: Find the acceleration of a body that changes velocity from 0 to 20 m/s in 4 seconds. 2. Formula: Acceleration $a = \frac{\Delta v}{t}$. 3. Calculation: $a = \frac{20 - 0}{4} = 5$ m/s$^2$. 4. Explanation: Acceleration is change in velocity over time. --- 1. State the problem: Calculate the force acting on a 10 kg mass accelerating at 3 m/s$^2$. 2. Formula: Force $F = ma$. 3. Calculation: $F = 10 \times 3 = 30$ N. 4. Explanation: Force equals mass times acceleration. --- 1. State the problem: Find the work done when a force of 50 N moves an object 2 meters. 2. Formula: Work $W = Fd$. 3. Calculation: $W = 50 \times 2 = 100$ J. 4. Explanation: Work is force times distance moved in the direction of force. --- 1. State the problem: Calculate the power if 100 J of work is done in 5 seconds. 2. Formula: Power $P = \frac{W}{t}$. 3. Calculation: $P = \frac{100}{5} = 20$ W. 4. Explanation: Power is work done per unit time. --- 1. State the problem: Find the pressure exerted by a force of 200 N on an area of 4 m$^2$. 2. Formula: Pressure $P = \frac{F}{A}$. 3. Calculation: $P = \frac{200}{4} = 50$ Pa. 4. Explanation: Pressure is force divided by area. --- 1. State the problem: Calculate the density of a substance with mass 500 g and volume 250 cm$^3$. 2. Formula: Density $\rho = \frac{m}{V}$. 3. Calculation: $\rho = \frac{500}{250} = 2$ g/cm$^3$. 4. Explanation: Density is mass per unit volume. --- 1. State the problem: Find the kinetic energy of a 2 kg object moving at 3 m/s. 2. Formula: $KE = \frac{1}{2}mv^2$. 3. Calculation: $KE = \frac{1}{2} \times 2 \times 3^2 = 9$ J. 4. Explanation: Kinetic energy depends on mass and square of velocity. --- 1. State the problem: Calculate the potential energy of a 5 kg object raised 10 m above ground. 2. Formula: $PE = mgh$. 3. Calculation: $PE = 5 \times 9.8 \times 10 = 490$ J. 4. Explanation: Potential energy depends on mass, gravity, and height. --- 1. State the problem: Find the frequency of a wave with speed 340 m/s and wavelength 2 m. 2. Formula: $v = f \lambda$. 3. Calculation: $f = \frac{v}{\lambda} = \frac{340}{2} = 170$ Hz. 4. Explanation: Frequency is wave speed divided by wavelength. --- 1. State the problem: Calculate the refractive index if light speed in air is $3 \times 10^8$ m/s and in glass is $2 \times 10^8$ m/s. 2. Formula: $n = \frac{c}{v}$. 3. Calculation: $n = \frac{3 \times 10^8}{2 \times 10^8} = 1.5$. 4. Explanation: Refractive index is ratio of speed of light in air to speed in medium. --- 1. State the problem: Find the resistance of a wire with voltage 12 V and current 3 A. 2. Formula: $R = \frac{V}{I}$. 3. Calculation: $R = \frac{12}{3} = 4$ ohms. 4. Explanation: Resistance is voltage divided by current. --- 1. State the problem: Calculate the current if 24 C of charge passes a point in 6 seconds. 2. Formula: $I = \frac{Q}{t}$. 3. Calculation: $I = \frac{24}{6} = 4$ A. 4. Explanation: Current is charge per unit time. --- 1. State the problem: Find the energy used by a 100 W bulb in 2 hours. 2. Formula: $E = Pt$. 3. Calculation: $E = 100 \times 2 \times 3600 = 720000$ J. 4. Explanation: Energy is power times time (converted to seconds). --- 1. State the problem: Calculate the momentum of a 0.5 kg ball moving at 10 m/s. 2. Formula: $p = mv$. 3. Calculation: $p = 0.5 \times 10 = 5$ kg m/s. 4. Explanation: Momentum is mass times velocity. --- 1. State the problem: Find the time period of a pendulum with frequency 2 Hz. 2. Formula: $T = \frac{1}{f}$. 3. Calculation: $T = \frac{1}{2} = 0.5$ s. 4. Explanation: Time period is reciprocal of frequency. --- 1. State the problem: Calculate the heat energy required to raise temperature of 2 kg water by 10°C. Specific heat capacity of water is 4200 J/kg°C. 2. Formula: $Q = mc\Delta T$. 3. Calculation: $Q = 2 \times 4200 \times 10 = 84000$ J. 4. Explanation: Heat energy depends on mass, specific heat, and temperature change. --- 1. State the problem: Find the wavelength of a photon with energy $3.3 \times 10^{-19}$ J. Planck's constant $h = 6.63 \times 10^{-34}$ Js, speed of light $c = 3 \times 10^8$ m/s. 2. Formula: $E = \frac{hc}{\lambda}$. 3. Calculation: $\lambda = \frac{hc}{E} = \frac{6.63 \times 10^{-34} \times 3 \times 10^8}{3.3 \times 10^{-19}} = 6.03 \times 10^{-7}$ m. 4. Explanation: Wavelength is Planck's constant times speed of light divided by energy. --- 1. State the problem: Calculate the gravitational force between two 5 kg masses 2 m apart. Gravitational constant $G = 6.67 \times 10^{-11}$ N m$^2$/kg$^2$. 2. Formula: $F = G \frac{m_1 m_2}{r^2}$. 3. Calculation: $F = 6.67 \times 10^{-11} \times \frac{5 \times 5}{2^2} = 4.17 \times 10^{-10}$ N. 4. Explanation: Gravitational force depends on masses and distance squared. --- 1. State the problem: Find the efficiency of a machine that does 500 J of useful work from 2000 J input energy. 2. Formula: Efficiency $= \frac{\text{useful energy output}}{\text{total energy input}} \times 100$%. 3. Calculation: $= \frac{500}{2000} \times 100 = 25$%. 4. Explanation: Efficiency is ratio of useful output to input energy times 100. --- 1. State the problem: Calculate the frequency of a sound wave with wavelength 0.5 m and speed 340 m/s. 2. Formula: $f = \frac{v}{\lambda}$. 3. Calculation: $f = \frac{340}{0.5} = 680$ Hz. 4. Explanation: Frequency is speed divided by wavelength. ---