A van of mass 2000 kg is travelling at 10 m/s .calculate its kinetic energy . If its speed increases to 20 m/s by how much amount does its kinetic energy increases?

Options

A. 25 kj
B. 75 KJ
C. 150 KJ
D. 300 KJ

Answer

To solve the problem, we will use the formula for kinetic energy (KE), which is given by:

\[ KE = \frac{1}{2} mv^2 \]

where:
- \( KE \) is the kinetic energy,
- \( m \) is the mass of the object,
- \( v \) is the velocity of the object.

### Step 1: Calculate the initial kinetic energy at 10 m/s.

Given:
- Mass of the van, \( m = 2000 \, \text{kg} \)
- Initial speed, \( v_1 = 10 \, \text{m/s} \)

Using the formula:
\[ KE_1 = \frac{1}{2} m v_1^2 \]
Substituting the values:
\[ KE_1 = \frac{1}{2} \times 2000 \, \text{kg} \times (10 \, \text{m/s})^2 \]
Calculating:
\[ KE_1 = \frac{1}{2} \times 2000 \times 100 = 100000 \, \text{J} \]
So, the initial kinetic energy \( KE_1 = 100000 \, \text{J} \).

### Step 2: Calculate the final kinetic energy at 20 m/s.

Now, we need to calculate the kinetic energy when the speed increases to 20 m/s.

Given:
- Final speed, \( v_2 = 20 \, \text{m/s} \)

Using the formula:
\[ KE_2 = \frac{1}{2} m v_2^2 \]
Substituting the values:
\[ KE_2 = \frac{1}{2} \times 2000 \, \text{kg} \times (20 \, \text{m/s})^2 \]
Calculating:
\[ KE_2 = \frac{1}{2} \times 2000 \times 400 = 400000 \, \text{J} \]
So, the final kinetic energy \( KE_2 = 400000 \, \text{J} \).

### Step 3: Calculate the increase in kinetic energy.

To find the increase in kinetic energy, we subtract the initial kinetic energy from the final kinetic energy:
\[ \Delta KE = KE_2 - KE_1 \]
Substituting the values:
\[ \Delta KE = 400000 \, \text{J} - 100000 \, \text{J} = 300000 \, \text{J} \]

### Final Answer:
The increase in kinetic energy when the speed increases from 10 m/s to 20 m/s is \( 300000 \, \text{J} \).

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