What will be the velocity-distance graph of constant acceleration?

Question

What will be the velocity-distance graph of constant acceleration?

Answer 1

it should be exponentially going upwards--similar to half a 'U' or a 'J'

Answer 2

acceleration is defined as the time derivative of velocity, dv/dt

if it is constant acceleration, then dv/dt = constant

constant slope = linear /straight line

intuitively, if it was exponential, with distance on the x axis, then the faster you were travelling, the less distance youd be covering!!!

Arguing that the relationship is anything but linear is stating that the velocity is changing at a continually different rate, which negates the assumption of constant acceleration.

Answer 3

It'll be a straight line, not parallel to either axis.

I mean, a straight line, passing through origin. This is because constant acceleration mean regular change of velocity.

Answer 4

Distance is the integral of velocity (area). Acceleration is the differential of velocity (slope). Now, you know you have a constant acceleration, lets make it C. To go from constant acceleration to speed, you integrate C. Thus getting C(t) m/s, where t is time. Distance is yet another integral, but of velocity which we know is C(t). So for distance you have 1/2C(t)p2. So to graph velocity against distance, you must take into account, that distance changes with the power of 2 of time, and velocity to the power of one of time. Thus, on the graph, the slope will start high, and then in a exponential curve slow down as you move on the distance axis.

Answer 5

For constant acceleration

v^2 = u^2 + 2as

The graph goes exponentially upward.

Answer 6

The graph should be a straight line.