Correct option is C
The correct answer is (c) v² − u² = 2as
Explanation:
• Kinetic energy is the energy possessed by an object due to its motion and is given by the formula:
Kinetic Energy = 1/2 × m × v².
• To derive this expression, we consider the work done in accelerating an object of mass m from an initial velocity u to a final velocity v.
• Work done is defined as force × displacement, that is:
Work = F × s.
• According to Newton’s Second Law, force F = m × a.
• Substituting this in the work equation gives:
Work = m × a × s.
• From the third equation of motion, we have:
v² − u² = 2 × a × s,
which can be rearranged to give:
s = (v² − u²) / (2a).
• Substituting this value of s into the work equation:
Work = m × a × (v² − u²) / (2a)
= 1/2 × m × (v² − u²).
• If the object starts from rest, that is u = 0, then:
Work = 1/2 × m × v².
• Since work done is equal to kinetic energy, the kinetic energy of the object is 1/2 × m × v².
Information Booster:
• According to the Work–Energy Theorem, the net work done on an object is equal to the change in its kinetic energy.
• Kinetic energy is a scalar quantity and is always positive or zero. It can never be negative because mass is always positive and the square of velocity is always positive.
Additional Knowledge:
• s = u × t + 1/2 × a × t² (Option a):
This is the second equation of motion, used to calculate displacement when time, initial velocity, and acceleration are known.
• a = (v − u) / t (Option b):
This is the definition of acceleration and represents the rate of change of velocity.
• v = u + a × t (Option d):
This is the first equation of motion, relating final velocity, initial velocity, acceleration, and time.
