## anonymous one year ago For what kind of motion are the instantaneous and average velocities equal? Why is the answer constant-velocity motion?

1. anonymous

2. anonymous

@DanJS

3. anonymous

because there is no acceleration when an object is moving with constant velocity so the instantaneous velocity is constant. If velocity isn't changing, the average over any interval is equal to the velocity at any specific time.

4. anonymous

then is it possible for an object's acceleration to be zero if the velocity if zero

5. anonymous

@Zale101

6. Abhisar

You can't confidently say that if acceleration is zero then velocity will surely be zero or if velocity is zero then acceleration will surely be zero. Like suppose a car is moving with a constant velocity then it's in uniform motion i.e. it has a velocity but no acceleration also think what happens when we throw a ball vertically above the ground, at a instant after attaining certain height its velocity becomes zero but it is still experiencing an acceleration (acceleration due to gravity) towards the ground so a body can have a zero velocity but still be accelerated.

7. anonymous

ok. how can you determine the speed of an object with the acceleration

8. Abhisar

$$\color{blue}{\text{Originally Posted by}}$$ @prguan For what kind of motion are the instantaneous and average velocities equal? Why is the answer constant-velocity motion? $$\color{blue}{\text{End of Quote}}$$ Suppose a car is moving with an accelerated motion such that its acceleration is $$\sf 1 m/s^2$$. Now let's note its velocity at different instants. Time Velocity 0 0 1 1 2 2 3 3 We see that its instant velocity at different instants of time will be different like, 1, 2 and $$\sf 3 m/s$$ but its average velocity will be 3m/s $$\sf (\frac{1+2+3}{3})$$

9. anonymous

why is the average velocity 3m/s (1+2+3)=6 6/3 is 2

10. Abhisar

No I am sorry, average velocity will be equal to $$\sf \frac{Total~Distance}{Total~Time}$$ And in the above case total distance = $$\sf (1 \times 1) +(1\times 2)+(1\times 3)$$ Total time = 3 seconds, so average velocity = 2m/s

11. Abhisar

Now, let's consider the case of a car going through a constant velocity of say 3 m/s i.e. it has no acceleration. Right? Let's do the same experiment and note its velocities at various instants of time. Time Velocity 0 0 1 3 2 3 3 3 So we see that velocity this car is same at all the instant of times and not only that its average velocity is also same as its instantaneous velocity. Check this by finding out its average velocity as i did in the above table.

12. anonymous

oh ok i though to find acceleration it was distance/ time

13. Abhisar

No, Distance/Time = Velocity and this formula is only applicable when the object is moving with constant velocity i.e. it has zero acceleration. To find acceleration you can use formula, V=U+at, where, V= final velocity U= initial velocity a= acceleration t=time

14. anonymous

so final velocity= initial velocity + acceleration x time x where is where- displacement

15. anonymous

what does where represent?

16. Abhisar

No where is nothing c:

17. anonymous

im confused

18. Abhisar

No, Distance/Time = Velocity and this formula is only applicable when the object is moving with constant velocity i.e. it has zero acceleration. To find acceleration you can use formula, $$\boxed{V=U+at}$$ Where, the symbols has following meaning V= final velocity U= initial velocity a= acceleration t=time

19. Abhisar

Is it clear now?

20. anonymous

i guess