If velocity is constant at 100 km/h [N], what is the second derivative of velocity?

Question

Would there be one?

Answer 1

zero (zero to the power of a thousand zeros and when i talk about zero i mean zero) hahahahahaha... it will be zero.

Answer 2

Suppose we have S = some distance.

The change is S, del S, over time, del t, is called velocity (v). Thus, v = del S/del t = (S1 - S0)/(t1 - t0) = 100 km/hr. This is the first derivative result.

The change in velocity del v over time del t is called acceleration (a). Thus a = del v/del t = (v1 - v0)/del t = 0/del t = 0; where v1 = v0, the beginning and ending velocities are the same since velocity is constant. This is the second derivative result when v1 = v0 or more succinctly v = constant.

In general, any derivative of a constant will equal zero. Why? Because a derivative is about change and, if there is no change, then zero means there is no change.

To answer your question directly, the value would be zero and, yes, there is one, but it's value is zero. del v/del t = 0 is a perfectly valid statement. Later, when you get integrals, you will find this out.

Answer 3

If something is constant, then the first and second derivative is zero. The derivative is the rate of change over time and the velocity is not changing.

Answer 4

The second derivative of a displacement function is acceleration. Velocity is the first derivative of a displacement function. If velocity is constant, then there is no acceleration. That means, derivative of a constant is zero, so is the acceleration when velocity is constant, and so is the second derivative of velocity.

Look for your formulas and prove it for yourself.

Answer 5

The first derivative of velocity gives acceleration and this in your case is zero, then what do you think the second derivative would be, work on the mathematics (derivations) you will know it.

Answer 6

If it's constant, the first derivative (and all subsequent ones) is constant and 0.