A question i was given says "what is the instantaneous velocity of the car at this time" and i already know that the average velocity at that time was 15 but im not sure what instantaneous velocity means and how to calculate it so could someone please explain that to me? ty
- Andrew SmithLv 74 weeks ago
Average velocity and instantaneous velocity are closely related.
Average velocity is the change in velocity over a substantial time interval divided by that interval. Instantaneous velocity is the change in velocity over an interval approaching zero divided by that small interval.
There CANNOT BE an average velocity AT a time. The average velocity MUST be over the span between two times. ie "from rest to time t the average velocity is v." is correct but "the average velocity AT time t" is meaningless.
Now the instantaneous velocity can be calculated from the slope of a velocity time graph. It can be calculated from the average velocity if we know the initial velocity and we also know that the acceleration is constant.
if Vav = (final + initial)/ 2 then Final = 2 * Vav - initial.
Starting from rest the initial velocity is zero so the final instantaneous velocity would THEN be 2 * average velocity.
- Anonymous4 weeks ago
If the initial (instantaneous) velocity was u
and the final (instantaneous) velocity was v
and there was uniform acceleration in between
(meaning u and v have the same direction),
avg v = ½(u + v)
final velocity v = (2 * avg v) - u
So if you know the initial velocity and the average velocity, then you know the final velocity.
Again, assumes uniform acceleration.
Other than this case, you need the velocity function as was expressed earlier.
- tentofieldLv 74 weeks ago
Velocity is a vector and has speed and direction. "15" is neither a speed nor a velocity. 15 metres per second is a speed, 15 m/s to the northeast is a velocity. A car travelling at an average speed of 15m/s could vary in its speed over the distance between 10m/s and 20m/s. The instantaneous speed is the speed at any one moment on the journey.
Roads are often not straight. While the overall direction of the trip might be northeast and the average velocity was 15m/s to the northeast, at any one moment the car could be heading north or east so while the average velocity is 15m/s to the northeast, the instantaneous velocity at any one point might be 15m/s to the north.
- 4 weeks ago
If you have the function for the position, you take the derivative and apply it at some value of x (or t or whatever). That will give you the instantaneous velocity (velocity is the change in position divided by the change in time).
Without a function, I can't tell you what the instantaneous velocity is at any time.
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- MorningfoxLv 74 weeks ago
Instantaneous velocity just means the velocity at some instant of time. BTW, average velocity can not be just "15". You need to say if it is meters per hour, or miles per second, or something like that. Also, velocity includes direction. A velocity of 15 meters per second straight up, is a lot different from 15 miles per week, to the north.