There's a car that accelerates by 10 m/s^2, why doesn't its speed become higher than the speed of light?

This is a very popular question. We know, courtesy of Einstein, that as anything goes faster, its apparent mass increases and it becomes harder to accelerate. The increase gets worse the faster we go, the mass becomes s the rest-mass /sqrt(1 - v^2/c^2) where v is the speed and c the speed of light. This mass is infinite when v gets to c - so clearly we can never get there.

This was considered extremely weird when the idea was first published in 1905 but has been confirmed many times by experiments and measurements.

To look into this some more, wikipedia the Special Theory of Relativity.

Let us look at it this way.

Assuming that you have a car which is provided with a 300HP engine and the car including its passengers weigh 3220 lbs, a coefficient of friction between the tires and the road of 0.2.

The total power available is:

P = 300 x 550 = 155000 ft -lbs /sec

The force of friction is:

Ff = 0.2 x 3220 = 644 lbs

Assuming a frontal area of the car of 4 ft x 6 ft, the wind force at velocity v, in miles per hour, is :

Fw = 0.003 x 24 x v^2

Thus:

(644 + 0.072v^2) v x (22/15) = P = 165000

v^3 + 8944v = 1562500

v = 238.08m/h

The above calculation shows that regardless of the maximum acceleration that the car can attain, its speed is limited by the available power to overcome friction and wind resistance. The acceleration of 10m/sec^2 (32.8ft/sec^2) can not be maintained. As the speed of the car increase, the resistance increases on a square variation, hence the acceleration dies down until the car would be moving at its maximum attainable speed as limited by its available power.

there is a theory that the closer your speed to the speed of light, the higher your mass becomes. That means, to achieve the speed of light, an object must be at the infinite mass, and that is theoretically impossible.

cmiiw.

well theoretically it can happen but in physical point of view

the speeding car is retarded by friction of both air and ground

the tires due to high revolution rate can melt or rip apart

besides the temperature will be very high due to high velocity

suppose you are given the chance to travel at the speed of light nothing of yours will remain in one piece when you reach the finish point

the above example was given for demonstration purpose only

hope this was helpful