# What happens when velocities comparable to the speed of light are involved in an observation? a. Newton’s second law of motion, F = ma , governs the motion of the object. b. Newton’s second law of motion, F = ma , no longer governs the dynamics of the object. c. Such velocities cannot be determined mathematically. d. None of the above

What happens when velocities comparable to the speed of light are involved in an observation?
a. Newton’s second law of motion, F = ma , governs the motion of the object.
b. Newton’s second law of motion, F = ma , no longer governs the dynamics of the object.
c. Such velocities cannot be determined mathematically.
d. None of the above
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The branch of classical mechanics which deals with velocities that we encounter in our daily lives is called Newtonian mechanics. But once the velocity becomes comparable to the speed of light, the laws of Newtonian mechanics don not hold anymore. This is when we enter the realm of Special Theory of Relativity. The major difference between Newtonian Mechanics and Special Theory of relativity is that The Special Theory of Relativity does not consider time to be universal for all observers. It says that just like the spacial variables, time is also relative to observers in different frames of reference.
The Special theory of Relativity also infers that for objects moving at velocities, comparable to the speed of light, the mass is no longer a constant quantity, rather, it becomes a velocity dependent quantity.
For velocity v of an object comparable to speed of light c, its mass m varies as follows
$m=\frac{{m}_{0}}{\sqrt{1-\frac{{v}^{2}}{{c}^{2}}}}$
where ${m}_{0}$ is its rest mass.
Thus we see that Newton's second law of motion no longer governs the dynamics of the object.
(b) Newton's second law of motion no longer governs the dynamics of the object.