The energy required to accelerate a car from 10 m/s to 20 m / s is how many times the energy required to accelerate the car from rest to 10 m /s

Options

A. Work done on the object in 30 s is zero
B. 2 W
C. 3 W
D. 4 W

Explanation

To solve the problem of finding how many times the energy required to accelerate a car from 10 m/s to 20 m/s is compared to the energy required to accelerate the car from rest to 10 m/s, we can follow these steps:

### Step 1: Understand the Concept of Work Done
The work done (energy required) to accelerate an object is equal to the change in kinetic energy (KE). The kinetic energy of an object is given by the formula:
\[ KE = \frac{1}{2} mv^2 \]
where \( m \) is the mass of the object and \( v \) is its velocity.

### Step 2: Calculate Work Done from Rest to 10 m/s
1. **Initial velocity (u)** = 0 m/s (the car starts from rest)
2. **Final velocity (v)** = 10 m/s
3. The work done (W) to accelerate from rest to 10 m/s is:
\[ W = KE_{final} - KE_{initial} = \frac{1}{2} m (10^2) - \frac{1}{2} m (0^2) \]
\[ W = \frac{1}{2} m (100) = 50m \]

### Step 3: Calculate Work Done from 10 m/s to 20 m/s
1. **Initial velocity (u')** = 10 m/s
2. **Final velocity (v')** = 20 m/s
3. The work done (W') to accelerate from 10 m/s to 20 m/s is:
\[ W' = KE_{final} - KE_{initial} = \frac{1}{2} m (20^2) - \frac{1}{2} m (10^2) \]
\[ W' = \frac{1}{2} m (400) - \frac{1}{2} m (100) \]
\[ W' = \frac{1}{2} m (400 - 100) = \frac{1}{2} m (300) = 150m \]

### Step 4: Compare the Two Work Done Values
Now, we need to find how many times \( W' \) is compared to \( W \):
\[ \frac{W'}{W} = \frac{150m}{50m} \]
The mass \( m \) cancels out:
\[ \frac{W'}{W} = \frac{150}{50} = 3 \]

### Conclusion
The energy required to accelerate the car from 10 m/s to 20 m/s is **3 times** the energy required to accelerate the car from rest to 10 m/s.