Speed Calculation Using Kinetic Energy
The problem asks for the speed of a body given its mass and kinetic energy. We are provided with the following information:
- Mass of the body, \(m = 4 \text{ kg}\)
- Kinetic Energy, \(KE = 72 \text{ J}\)
The relationship between kinetic energy, mass, and speed is defined by the kinetic energy formula:
\( KE = \frac{1}{2}mv^2 \)
To determine the speed (\(v\)), we need to rearrange this formula.
Calculating the Speed
Follow these steps to find the speed:
- Isolate \(v^2\) in the formula: Multiply both sides by 2 and divide by \(m\).
\( v^2 = \frac{2 \times KE}{m} \)
- Substitute the given values for \(KE\) and \(m\):
\( v^2 = \frac{2 \times 72 \text{ J}}{4 \text{ kg}} \)
- Simplify the expression:
\( v^2 = \frac{144 \text{ J}}{4 \text{ kg}} \)
\( v^2 = 36 \frac{\text{J}}{\text{kg}} \)
Recall that \(1 \text{ J} = 1 \text{ kg} \cdot \text{m}^2/\text{s}^2\). Thus, the units simplify to \(\text{m}^2/\text{s}^2\).
\( v^2 = 36 \text{ m}^2/\text{s}^2 \)
- Find the speed (\(v\)) by taking the square root:
\( v = \sqrt{36 \text{ m}^2/\text{s}^2} \)
\( v = 6 \text{ m/s} \)
The calculated speed of the body is 6 m/s.
Similar Questions
If a force ‘F’ acts on a body such that body gets displaced through the distance ‘x’ in the direction of the force, then the work done by the force is ____________.
The kinetic energy of a moving object is dependent on which of the following quantities:
i) Mass of the body
ii) Square of the velocity
iii) PressureWhich of the following statements refer/s to the law of conservation of energy?
Statements:
I) Energy can be converted from one form to another form of energy.
II) Energy can neither be created nor destroyed.
The work done in moving 10 coulomb charges across the potential difference of 5 volts is______.
- Mechanical energy is the sum of _______.
- A spring when compressed by 4 cm has 2 J energy stored in it. The force required to extend it by 8 cm will be
- Dams are constructed to collect water flowing in high altitude rivers. The stored water has a lot of
The work done by a constant force of 5 Newton acting on a body is 5 joules. The Displacement of the body in the direction of the applied force is ______.
The kinetic energy of a body of mass 2 kg, which is moving with the constant velocity 5 m/sec, is .............
- A machine does 1000 J of work in 5 seconds. Its power is:
Important Questions from Work and Energy
If a force ‘F’ acts on a body such that body gets displaced through the distance ‘x’ in the direction of the force, then the work done by the force is ____________.
The kinetic energy of a moving object is dependent on which of the following quantities:
i) Mass of the body
ii) Square of the velocity
iii) PressureWhich of the following statements refer/s to the law of conservation of energy?
Statements:
I) Energy can be converted from one form to another form of energy.
II) Energy can neither be created nor destroyed.
The work done in moving 10 coulomb charges across the potential difference of 5 volts is______.
- Mechanical energy is the sum of _______.
