why is a parabola formed when a graph of distance vs. velocity is plotted against each other?

Answer 1

Not every distance/velocity relation forms a parabola. You only get a parabola if you have constant acceleration.

Suppose you have a constant acceleration of a (meters per second) per second.
Suppose you have an initial velocity of b (meters per second)
Suppose you have an initial position of c meters from the origin.
Let t be the time elapsed, in seconds.

Then the equation for your position is:
a*t^2 + b*t + c = 0.

This is a 2nd degree polynomial, so obviously it forms a parabola.

Answer 2

when we plot distance vs velocity it forms a straight line having a positive slope . It doen`t mean that it doesn`t follow parabola. It also forms parabola when a body which is falling having a final velocity the body reaches the ground , then we will attain a parabola when we plot distance vs velocity the shape lokk like parabola.

WHEN THE BODY IS FALLING FROM A POINT THEN THE BODY ATTAINS A MAXIMUM VELOCITY AT A PARTICULAR POINT AND AFTER THAT IT DECREASES SO WE CAN GET A SHAPE OF PARABOLA.

Answer 3

It should look like a parabola because the speed is increasing,
and the slope is increasing would be the main reason.
In nature, approximations of parabolae and paraboloids are found in many diverse situations. The most well-known instance of the parabola in the history of physics is the trajectory of a particle or body in motion under the influence of a uniform gravitational field without air resistance (for instance, a baseball flying through the air, neglecting air friction). The parabolic trajectory of projectiles was discovered experimentally by Galileo in the early 17th century, who performed experiments with balls rolling on inclined planes. The parabolic shape for projectiles was later proven mathematically by Isaac Newton. For objects extended in space, such as a diver jumping from a diving board, the object itself follows a complex motion as it rotates, but the center of mass of the object nevertheless forms a parabola. As in all cases in the physical world, the trajectory is always an approximation of a parabola. The presence of air resistance always distorts the shape, for example, although at low speeds, the shape is a good approximation of a parabola. At higher speeds, such as in ballistics, the shape is highly distorted and does not resemble a paAnother situation in which parabola may arise in nature is in two-body orbits, for example, of a small planetoid or other object under the influence of the gravitation of the sun. Such parabolic orbits are a special case that are rarely found in nature. Orbits that form a hyperbola or an ellipse are much more common. In fact, the parabolic orbit is the borderline case between those two types of orbit.

Approximations of parabolas are also found in the shape of cables of suspension bridges. Freely hanging cables do not describe parabolas, but rather catenary curves. Under the influence of a uniform load (for example, the deck of bridge), however, the cable is deformed towards a parabola.rabola.

Paraboloids arise in several physical situations as well. The most well-known instance is the parabolic reflector, which is a mirror or similar reflective device that concentrates light or other forms of electromagnetic radiation to a common focal point. The principle of the parabolic reflector was discovered in the 3rd century BC by the geometer Archimedes, who, according to a legend of debatable veracity,[1] constructed parabolic mirrors to defend Syracuse against the Roman fleet, by concentrating the sun's rays to set fire to the decks of the Roman ships. The principle was applied to telescopes in the 17th century. Today, paraboloid reflectors can be commonly observed throughout much of the world in microwave and satellite dish antennas.

Paraboloids are also observed in the surface of a liquid confined to a container and rotated around the central axis. In this case, the centrifugal force causes the liquid to climb the walls of the container, forming a parabolic surface. This is the principle behind the liquid mirror telescope.

Answer 4

the distance time graph will be a parabola as the equation is s=ut+1/2at^2 is the equation of a parabola

Answer 5

You will have a parabola only when d = av^2 + bv + c or
v = ad^2 + bd + c. The first occurs if you have a constantly increasing or decreasing acceleration. I don't even want to speculate on the second.