Q1.
How much is the energy possessed by an object by virtue of its motion?
Answer
An object of mass m moving with speed v has kinetic energy K = ½mv2.
Take an object of mass m pushed by a constant force F from speed u to speed v over displacement s.
Kinematics: v2 = u2 + 2as, so s = (v2 – u2) / 2a
Work done: W = F × s = ma × (v2 – u2)/2a
W = ½m(v2 – u2) (Eq. 7.5)
By the work–energy theorem this is the change in the object's energy.
Starting from rest (u = 0), the whole of it is the kinetic energy gained:
K = ½mv2 (Eq. 7.6)
Kinematics: v2 = u2 + 2as, so s = (v2 – u2) / 2a
Work done: W = F × s = ma × (v2 – u2)/2a
W = ½m(v2 – u2) (Eq. 7.5)
By the work–energy theorem this is the change in the object's energy.
Starting from rest (u = 0), the whole of it is the kinetic energy gained:
K = ½mv2 (Eq. 7.6)
Why the square matters: K grows as v2, not as v. Doubling the speed of a vehicle makes its kinetic energy four times larger (Example 7.4), so the brakes must remove four times as much energy — which is why speed, not mass, is the biggest factor in road accidents.
Tip: kinetic energy has no direction. A ball moving east at 5 m s–1 and the same ball moving west at 5 m s–1 have exactly the same kinetic energy. Its unit is the joule: 1 J = 1 kg m2 s–2.