Question

A negative acceleration means that the speed of the object decreases. Explain why this statement can be incorrect????

Answer 1

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.

Answer 2

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.

Answer 3

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

Answer 4

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?

Answer 5

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

Answer 6

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

Answer 7

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

Answer 8

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?

Answer 9

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

Answer 10

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

Answer 11

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

Answer 12

Also, when is the Displacement negative??

Answer 13

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

Answer 14

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

Answer 15

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?

Answer 16

i mean aren't we usually finding the magnitude?

Answer 17

The magnitude of what?

Answer 18

displacement

Answer 19

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

Answer 20

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

Answer 21

*or

Answer 22

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?

Answer 23

this is how i interpreted this

Answer 24

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.