Question

An object of mass 15 kg is moving with a uniform velocity of \(4 \text{ ms}^{-1}\). What is the kinetic energy possessed by the object ?

• A. 100 J
• B. 120 J
• C. 130 J
• D. 15 J

Hint:

Formula for Kinetic Energy (KE): \(KE = \frac{1}{2}mv^2\). 1. Given: mass \(m = 15\) kg, velocity \(v = 4\) m/s. 2. Calculate \(v^2\): \(4^2 = 16\). 3. Substitute into the formula: \(KE = \frac{1}{2} \times 15 \times 16\). 4. Simplify: \(KE = 15 \times \frac{16}{2} = 15 \times 8\). 5. Result: \(KE = 120\) Joules (J).

Answer 1

The Correct Option is B

Concept: Kinetic energy (KE) is the energy possessed by an object due to its motion. It is given by the formula: \[ KE = \frac{1}{2} m v^2 \] where:
\(m\) is the mass of the object (in kilograms, kg).
\(v\) is the velocity (or speed) of the object (in meters per second, m/s or \(\text{ms}^{-1}\)).
KE is measured in Joules (J). Step 1: Identify the given values
Mass of the object, \(m = 15 \text{ kg}\)
Uniform velocity of the object, \(v = 4 \text{ ms}^{-1}\) (which is 4 m/s) Step 2: Substitute the values into the kinetic energy formula \[ KE = \frac{1}{2} \times m \times v^2 \] \[ KE = \frac{1}{2} \times 15 \text{ kg} \times (4 \text{ m/s})^2 \] Step 3: Calculate \(v^2\) \[ v^2 = (4)^2 = 16 \text{ (m/s)}^2 \text{ or } \text{m}^2\text{s}^{-2} \] Step 4: Calculate the kinetic energy \[ KE = \frac{1}{2} \times 15 \times 16 \] We can simplify the calculation: \(\frac{1}{2} \times 16 = 8\). \[ KE = 15 \times 8 \] \[ KE = 120 \] The unit of kinetic energy is Joules (J), since mass is in kg and velocity is in m/s. So, \(KE = 120 \text{ J}\). The kinetic energy possessed by the object is 120 J. This matches option (2).