## buggiethebug 2 years ago A negative acceleration means that the speed of the object decreases. Explain why this statement can be incorrect????

1. ghazi

the statement could be incorrect because just consider an example that still its acceleration so if its negative and if it persists then it will increase the speed in the reverse direction.

2. ghazi

so speed basically is reduced by retardation , speaking of negative acceleration also depends on the frame of reference, if your assumption is somewhat in an opposite direction of the frame then also you may get negative acceleration.

3. buggiethebug

but it all depends on the direction you choose as positive right, but I think the question is really asking why why is a negative acceleration means that the speed of the object is decreasing? how could this be wrong? it makes sense though

4. JamesJ

Because speed isn't velocity. For example, drop a book the the floor. If we assign vertical up to be the positive y direction say, then the acceleration is negative. Yet the speed of the book constantly increases. Why? Because the velocity of the book becomes larger and larger negative values. But as speed is the absolute value or magnitude of velocity, speed is increasing, even as velocity is decreasing. Make sense?

5. ghazi

in my first statement i stated that negative acceleration doesnt mean reduction in speed it is decided by frame of reference and your assumption of direction

6. JamesJ

Explicitly suppose you hold a book 1 meter off the floor and drop it at time t = 0. The acceleration is a = -g m/s^2 The velocity of the book is v = -gt m/s which decreases as t marches on But the *speed* of the book is speed = gt m/s which increases as t marches on

7. ghazi

by the way in case of free fall a= +g

8. buggiethebug

I get it, how speed isn't velocity, i think that makes more sense, as speed does not have direction , but if it were velocity, it would be a true statement right?

9. JamesJ

Yes, it would be. @ghazi, as we have defined the coordinate system here, with the up direction being positive, the acceleration is negative, i.e., a = -g

10. buggiethebug

but isn't a=-9.8m/s^2 if it's free falling? direction is up(+)

11. JamesJ

Yes, exactly. a = -g = -9.8 m/s^2

12. buggiethebug

Also, when is the Displacement negative??

13. JamesJ

Hence the velocity as a function of time is v(t) = -9.8t m/s

14. ghazi

velocity has direction and magnitude but speed has just magnitude @JamesJ oh sorry i didnt notice that, thats what i am saying it all depends on the reference and a = +g if object is falling on earth not a=-g but as he has stated different coordinate so here we can consider a=-g

15. JamesJ

It depends where we set displacement equal to zero. Suppose the floor is the zero and we drop the book from a height of 1 meter, you tell me: what is the displacement as a function of time t?

16. buggiethebug

i mean aren't we usually finding the magnitude?

17. JamesJ

The magnitude of what?

18. buggiethebug

displacement

19. ghazi

when you are supposed to find just magnitude its, distance and when you get direction included its displacement

20. JamesJ

Displacement like velocity is a vector quantity. Hence in one dimension like this book problem it can have a sign of positive of negative.

21. JamesJ

*or

22. buggiethebug

A rock is thrown up with a speed of 32.5km/h from a tree that is 15.75 m tall. How long will it take to hit the ground?

23. buggiethebug

this is how i interpreted this

24. JamesJ

You figure that out! Use the standard kinematic equations, in particular the one that gives displacement as sa function of time, initial velocity and acceleration.

25. buggiethebug

|dw:1360795426340:dw|

26. JamesJ

Yes

27. buggiethebug

i dont get what the displacement will be though

28. buggiethebug

It's hard to picture it

29. ghazi

well , displacement would be negative of the height of tree

30. buggiethebug

Howww and why would it be negative :S

31. ghazi

since the person is standing on tree so take that as the reference and below him take the height as negative so when stone goes up and comes back again it reaches the top of the tree , so basically the point from where it was thrown it got back there, therefore total displacement=0 but after that it keeps falling down so below that point height of the tree is negative for stone, as i said top of the tree is meant to be zero or starting point

32. JamesJ

It depends where you define displacement to be equal to zero. You can make it zero where the ground is, or you can make it zero from the point on the tree where the rock is thrown. Or you can make displacement= 0 at 100 km/s above the ground. In general, it's best to choose the point where displacement = 0 to be as convenient as possible. In this case, I would choose it to be the level of the ground.

33. buggiethebug

OHHHHHHHH

34. JamesJ

*100 km

35. ghazi

|dw:1360795675315:dw|

36. JamesJ

Ghazi in his diagram has chosen zero to be at the height where the rock is thrown. Nothing wrong with that choice.

37. Vincent-Lyon.Fr

For linear motion, speed will increase if acceleration and velocity are both positive or if they are both negative. Speed will decrease if velocity and acceleration have opposite signs.

38. buggiethebug

Vincent: I'm confused

39. JamesJ

@vincent. Pottery barn rule --> OpenStudy rule: You answer it, you explain it! :-)