Question

A toy car of mass 100 g is moving with velocity of $(\hat{i}+2\hat{j}-3\hat{k})$ m/s, then the kinetic energy of the car is

• A. $7 \text{ J}$
• B. $70 \text{ J}$
• C. $0.7 \text{ J}$
• D. $0.07 \text{ J}$

Hint:

Tip: For velocity vectors, use magnitude to compute speed before applying the kinetic energy formula.

Answer 1

The Correct Option is C

Mass $m = 100 \text{ g} = 0.1 \text{ kg}$. Velocity vector is $\vec{v} = \hat{i}+2\hat{j}-3\hat{k}$, so speed: \[ |\vec{v}| = \sqrt{1^2 + 2^2 + (-3)^2} = \sqrt{14}, \quad v^2 = 14 \] Kinetic energy: \[ KE = \frac{1}{2}mv^2 = \frac{1}{2} \cdot 0.1 \cdot 14 = 0.7 \text{ J} \] So, the kinetic energy of the toy car is $0.7$ J.

Answer 2

Step 1: Identify given data
Mass of toy car, \(m = 100 \text{ g} = 0.1 \text{ kg}\)
Velocity vector, \(\vec{v} = \hat{i} + 2\hat{j} - 3\hat{k} \text{ m/s}\)

Step 2: Calculate the magnitude of velocity
\[ v = \sqrt{1^2 + 2^2 + (-3)^2} = \sqrt{1 + 4 + 9} = \sqrt{14} \]

Step 3: Use the kinetic energy formula
\[ KE = \frac{1}{2} m v^2 \]
Since \(v^2 = 14\),
\[ KE = \frac{1}{2} \times 0.1 \times 14 = 0.7 \text{ J} \]

Step 4: Conclusion
The kinetic energy of the toy car is \(0.7 \text{ J}\).