Speed is scalar (it doesn't have direction), and the magnitude of velocity (a vector).
The first derivative of velocity is acceleration, therefore the first derivative of speed is the magnitude of acceleration.
The derivative of speed is acceleration, which measures how quickly an object's velocity is changing. It is calculated by finding the rate of change of velocity with respect to time. Mathematically, acceleration is the second derivative of position with respect to time.
The same way you get the second derivative from any function. Assuming you have a function that expresses potential energy as a function of time, or perhaps as a function of position, you take the derivate of this function. This will give you another function. Then, you take the derivate of this derivative, to get the second derivative.
Derivatives for displacement refer to the rate of change of an object's position with respect to time. It can be calculated by finding the first derivative of the position function. The first derivative of displacement gives the object's velocity, while the second derivative gives the acceleration.
The speed of an object at a particular moment in time is called instantaneous speed. It is the rate at which an object is moving at an individual point in time.
Hum, it cannot. As acceleration is the first derivative of the speed, if the speed is constant the derivative is null, if the speed is decreasing the derivative is negative. When talking about all this stuff we take into account the instantaneous values (instant speed, instant acceleration). Note that when you slow down, you slow down overall but can locally in time accelerate a little bit, let's say during 1/10th of a sec because you reached a partion of the road which was sloping. However this does not change the fact that when the speed decrease, the acceleration is negative.
First derivative of distance with respect to time.
The derivative of speed is acceleration, which measures how quickly an object's velocity is changing. It is calculated by finding the rate of change of velocity with respect to time. Mathematically, acceleration is the second derivative of position with respect to time.
change in speed is acceleration. change in speed is the slope of the speed versus time graph, or the derivative of such.
All it means to take the second derivative is to take the derivative of a function twice. For example, say you start with the function y=x2+2x The first derivative would be 2x+2 But when you take the derivative the first derivative you get the second derivative which would be 2
2x is the first derivative of x2.
Yes.
2x is the first derivative of x2.
Afetr you take the first derivative you take it again Example y = x^2 dy/dx = 2x ( first derivative) d2y/dx2 = 2 ( second derivative)
well, the second derivative is the derivative of the first derivative. so, the 2nd derivative of a function's indefinite integral is the derivative of the derivative of the function's indefinite integral. the derivative of a function's indefinite integral is the function, so the 2nd derivative of a function's indefinite integral is the derivative of the function.
Average Speed = Total Distance/Total Time.Instantaneous Speed = Derivative of Distance with respect to Time.
The first derivative is the rate of change, and the second derivative is the rate of change of the rate of change.
in case of derivative w.r.t time first derivative with a variable x gives velocity second derivative gives acceleration thid derivative gives jerk