A car of mass 800kg attains a speed of 25m/s in 20secs. The power developed in the engine is?

1. Analyze the Question

We are given the mass of a car ($m = 800\text{ kg}$), its final velocity ($v = 25\text{ m/s}$), and the time taken to reach that velocity ($t = 20\text{ s}$). We assume the car starts from rest ($u = 0\text{ m/s}$). We need to calculate the power developed by the engine.

2. Explain the Concept

Power is defined as the rate at which work is done or the rate at which energy is transferred.

• Work Done ($W$): In this case, the work done is equal to the change in kinetic energy of the car. • $W = \Delta K.E. = \frac{1}{2}mv^2 - \frac{1}{2}mu^2$
• Power ($P$): Power is Work divided by time. • $P = \frac{W}{t}$

3. Show the Solution

Step 1: Calculate the Work Done (Kinetic Energy gained) Since the car starts from rest ($u = 0$): $W = \frac{1}{2} \times m \times v^2$ $W = \frac{1}{2} \times 800 \times (25)^2$ $W = 400 \times 625$ $W = 250,000\text{ Joules}$ (or $2.5 \times 10^5\text{ J}$)

Step 2: Calculate the Power $P = \frac{W}{t}$ $P = \frac{250,000}{20}$ $P = 12,500\text{ Watts}$

Step 3: Convert to Standard Form $12,500 = 1.25 \times 10^4\text{ W}$

4. Identify the Answer

Comparing our result to the given options: A. $1.25 \times 10^4\text{ W}$ B. $2.50 \times 10^4\text{ W}$ C. $1.25 \times 10^6\text{ W}$ D. $2.50 \times 10^6\text{ W}$

The calculated value matches option A.

5. Tip

When solving power problems involving motion, always check if you are given force or velocity. If you have force and velocity, use $P = Fv$. If you have mass, velocity, and time (like in this question), calculating the change in kinetic energy and dividing by time is the most direct path to the answer. Don't forget to convert your final answer to standard form as required by JAMB!