Question:
If the speed of a vehicle increases by 2m/s, its kinetic energy is doubled. Then, the original speed of the vehicle is:
If the speed of a vehicle increases by 2m/s, its kinetic energy is doubled. Then, the original speed of the vehicle is:
Updated On: Apr 30, 2024
- \(\sqrt{2}\)+1 m/s
- \(2(\sqrt{2}-1)\) m/s
- \(2(\sqrt{2}+1)\) m/s
- \(\sqrt2(\sqrt{2}+1)\) m/s
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The Correct Option is C
Solution and Explanation
The correct option is C)
Let the initial speed of the vehicle be v \(\frac{m}{s}\)
According to the question :
2 (\(\frac{mv^2}{2}\)) = \(\frac{m(v+2)^2}{2}\)
\(v^2=4+4v\)
\(v^2-4v-4=0\)
v = 2(\(\sqrt2\)+1) \(\frac{m}{s}\)
Let the initial speed of the vehicle be v \(\frac{m}{s}\)
According to the question :
2 (\(\frac{mv^2}{2}\)) = \(\frac{m(v+2)^2}{2}\)
\(v^2=4+4v\)
\(v^2-4v-4=0\)
v = 2(\(\sqrt2\)+1) \(\frac{m}{s}\)
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Concepts Used:
Kinetic energy
Kinetic energy of an object is the measure of the work it does as a result of its motion. Kinetic energy is the type of energy that an object or particle has as a result of its movement. When an object is subjected to a net force, it accelerates and gains kinetic energy as a result. Kinetic energy is a property of a moving object or particle defined by both its mass and its velocity. Any combination of motions is possible, including translation (moving along a route from one spot to another), rotation around an axis, vibration, and any combination of motions.
