What is the formula for instantaneous speed?

Question

it is a science question. I can't seem to find the equation/formula anywhere.

Answer 1

Click on this link. Scroll down to the section called "Average Speed". The formula for instantaneous speed is derived there:
http://en.wikipedia.org/wiki/Speed

Answer 2

What Is Instantaneous Speed

Answer 3

If you have an equation for the speed, just plug in the coordinate of where you want the instantaneous speed at and that's the answer.
If you have an equation for location as a function of time, you need to take the first derivative and plug in the time.

If you're equation for speed is x^2 +x + 4, and you want the instantaneous speed at x = 6, just plug in 6 for x and that's your answer.

If your equation for x as a function of time is,

2 * t^2, take the 1st derivative which is 4*t and plug in the value for t you're interested in and you have the answer

Answer 4

Instantaneous speed is also your velocity (distance per time) at any given point in time. Usually velocity is given as meters/sec, miles/hour, feet/min, etc.... In order to calculate it you need more information like the distance covered in such time. If the velocity was the same the whole time, then just divide the distance by the time and you will have velocity. Also, if you have the equation for acceleration, then the first derivative of the equation will give you the velocity over the course of time that the equation covers. Hope that helps.

Answer 5

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Yes - depending on the type of system and the information you have. E.g. if you have a velocity-time graph, you can read-off the instantaneous speed at any time directly from the graph. E.g. if you have a displacement-time graph, you can determine the gradient of the tangent at the time of interest. E.g. if you know initial velocity (u), average acceleration (a) and elapsed time (t), you can calculate it using v = u+at E.g. if you know initial velocity (u), average acceleration (a) and displacement (s), you can calculate it using v = √[u² + 2as] E.g if you are talking about simple harmonic motion where x=Acos(ωt), then v = -ωAsin(ωt) E.g if you know the position of an object as a function of time, x(t), then v = dx/dt. And so on....

Answer 6

speed = velocity = change in distance / change in time
there is no universal "instantaneous speed" equation
You can check the slope of a line or curve at any point by taking its derivative.

Example:
for y = x^2 + 2x + 1
the derivative = dy/dx = 2x+ 2
to find the slope (velocity) at point (1,2) then replace x = 1 to get the slope of 4.

hope that helps.

Answer 7

speed is just distance / time

the definition of instantaneous speed requires calculus
if f(t) is the displacement of an object as a function of time then

df(t) / dt = instantaneous speed

Answer 8

Maybe you are looking for the generic equations:

v=u+at

v^2=u^2+2as

s=ut+1/2at^2

v=current velocity (in this case also speed) in m/s
u=initial velocity (or speed) in m/s
a=acceleration in m/s^2
t=time in seconds
s=distance in m

Answer 9

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