Due to special relativity, this is not the case. At this point, many readers will question the validity of any answer which uses advanced, intimidating-sounding physics terms to explain a position. However, it is true. The relevant equation is v/c = tanh (at/c). One will find that in this equation, tanh(at/c) can never exceed or equal 1. This means that velocity can never reach the speed of light, regardless of how long one accelerates for and the rate of the acceleration.
Astronomers have made experiments with pendulums which have been suspended from the interior of high buildings, and have exulted over the idea of being able to prove the rotation of the Earth on its "axis," by the varying direction taken by the pendulum over a prepared table underneath - asserting that the table moved round under the pendulum, instead of the pendulum shifting and oscillating in different directions over the table! But, since it has been found that, as often as not, the pendulum went round the wrong way for the "rotation" theory, chagrin has taken the place of exultation, and we have a proof of the failure of astronomers in their efforts to substantiate their theory, and, therefore, a proof that Earth is not a globe.
46) On a ball-Earth Cape Town, South Africa to Buenos Aries, Argentina should be a straight shot over the Atlantic following the same line of latitude across, but instead every flight goes to connecting locations in the Northern hemisphere first, stopping over anywhere from London to Turkey to Dubai. Once again these make absolutely no sense on the globe but are completely understandable options when mapped on a flat Earth.

Another point concerning timezones, the sun, and Earth: If the sun was a “spotlight” (very directionally located so that light only shines on a specific location) and the world was flat, we would see the sun even if it didn’t shine on top of us (as you can see in the drawing below). Similarly, you can see the light coming out of a spotlight on a stage in the theater, even though you—the crowd—are sitting in the dark. The only way to create two distinctly separate time zones, where there is complete darkness in one while there’s light in the other, is if the world is spherical.

 179) If the Earth were constantly spinning Eastwards 1000mph then airplane flight durations going Eastwards vs. Westwards should be significantly different. If the average commercial airliner travels 500mph, it follows that Westbound equatorial flights should reach their destination at approximately thrice the speed as their Eastbound return flights. In reality, however, the differences in East/Westbound flight durations usually amount to a matter of minutes, and nothing near what would occur on a 1000mph spinning ball Earth.
A "Standing Order" exists in the English Houses of Parliament that in the cutting of canals, &c., the datum line employed shall be a "horizontal line, which shall be the same throughout the whole length of the work." Now if the Earth were a globe, this "Order" could not be carried out: but, it is carried out: therefore it is a proof that the Earth is not a globe.
58) The Royal Belgian Geographical Society in their “Expedition Antarctique Belge,” recorded that during the most severe part of the Antarctic winter, from 71 degrees South latitude onwards, the sun sets on May 17th and is not seen above the horizon again until July 21st! This is completely at odds with the ball-Earth theory, but easily explained by the flat-Earth model. The Midnight Sun is seen from high altitudes in extreme Northern latitudes during Arctic summer because the Sun, at its inner-most cycle, is circling tightly enough around the polar center that it remains visible above the horizon for someone at such a vantage point. Likewise, in extreme Southern latitudes during Arctic summer, the Sun completely disappears from view for over 2 months because there at the Northern Tropic, at the inner-most arc of its boomerang journey, the Sun is circling the Northern center too tightly to be seen from the Southern circumference.
Astronomers tell us that, in consequence of the Earth's "rotundity," the perpendicular walls of buildings are, nowhere, parallel, and that even the walls of houses on opposite sides of a street are not! But, since all observation fails to find any evidence of this want of parallelism which theory demands, the idea must be renounced as being absurd and in opposition to all well-known facts. This is a proof that the Earth is not a globe.