The work done by a force on body of mass 5 kg to accelerate it in the direction of force from rest to 20 m/s2 in 10 second is
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Acceleration (a): The acceleration that causes a speed increase from 0 to 20 m/s in 10 seconds is calculated as:
a = v / t = 20 m/s / 10 s = 2 m/s2
Force (F): The force acting on the body, given mass (m) of 100 kg, is:
F = m * a = 100 N * 2 m/s2 = 200 N
Distance (s): The distance traveled in the given time (10 seconds) is:
s = 1/2 * a * t2 = 1/2 * 2 m/s2 * (10 s)2 = 100 m
Therefore,
- The acceleration is 2 m/s2.
- The force acting on the body is 200 N.
- The distance traveled in 10 seconds is 100 meters.
- 2x103 J
- 4x103 J
- 10-3 J
- 103 J
The Correct Option is D
Solution and Explanation
acceleration = \(\frac {final \ velocity - initial \ velocity}{time}\)
acceleration = \(\frac {20 -0}{10}\)= 2 m/s².
Force = mass × acceleration.
Given that the mass is 5 kg and the acceleration is 2 m/s²:
Force = 5 kg × 2 m/s² = 10 N.
Work = Force × Displacement × cos(θ).
Displacement = \(\frac {1}{2}\) × acceleration × time²
Displacement = \(\frac {1}{2}\) × 2 m/s² × (10 s)² = 100 m.
Work = 10 N × 100 m × 1 = 1000 J.
Therefore, the work done by the force is 1000 Joules (J).
The correct option is (D) 103 J.
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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.
