Two Questions regarding velocity and acceleration?

Question

1. If the velocity of a particle is zero, can its acceleration be non-zero?

2. Can an object having constant acceleration ever stop and stay stopped?

Answer 1

Both velocity and acceleration are measured with respect to time.

They are measured by the CHANGE of displacement in the former case and velocity in the latter case for a very brief interval of time.

Therefore, one cannot say any thing about their value unless one knows what happened before that instant of time and what happened after that instant of time for a brief interval of time.

Answer to your first question.

When we say the velocity is zero, the body is at rest at that instant of time.

Before and after that instant of time, ' what was its velocity"? It is not known and cannot be known until one tells the history of motion of the body.

ACCELERATION IS THE HISTORY OF THE MOTION OF THE OBJECT for a brief period of time.

If one says that the velocity is zero and acceleration IS ZERO at that instant, then the body is at rest at that instant and it was at rest before that instant and it will be at rest after that instant of time. {Note that before and after for a very brief interval of time}

If one says that the velocity is zero and acceleration IS NOT ZERO at that instant, the body is at rest at that instant of time and at once it will start its motion from its state of rest into a state of motion since the acceleration is not zero. Before that instant of time, the body was in motion but its velocity was reducing to zero and has come to stop at that instant of time when its value is zero.

Thus acceleration reveals the history of motion for a brief period.

Answer to your second question.

If you have understood the answer for first question, then the second question will not arise.


If there is acceleration at that instant, the velocity is of any value including zero velocity.

Before that instant of time, if the body had a velocity in the direction opposite to that of acceleration, then the body will come to stop at one instant and will move in the opposite direction.

Objects thrown up are at any time has a constant acceleration through out its path and even at its top most point when the velocity is zero; the object has the constant acceleration.



And if there is constant acceleration, the velocity of the body will be continuously changing. If the velocity was negative, at some instant of time, due to constant acceleration the velocity will become zero at one instant and then increases in the positive direction.

Also note that as long as there is acceleration there is no limit for the value of the velocity.

Acceleration is change in speed and hence cannot keep a body at rest or at any constant speed.

Since speed changes continuously, during the process of change it may attain a zero value too.

Answer 2

1. Yes. If the particle is moving in one direction and a force is applied in the direction to oppose the motion, the particle will eventually stop and reverse direction. At the instant the particle reverses direction, the velocity will pass through zero but the acceleration will remain constant at the value that was established when the force was applied.

2. No. The object can only pass through zero velocity. In order for the object to stop and remain stopped, the decelerating force must be reduced to zero at the moment the object stops. Once the object has both zero velocity and zero acceleration the acceleration is constant with a value of zero and the object remains stopped.

Answer 3

I'll say just the opposite of the previous two responders.

1. Yes! But its velocity can only be zero for an instant. A perfect example is when you throw a rock straight up in the air. Its acceleration is constantly 9.8m/s² during its entire trip (up and down); but its velocity is (momentarily) zero at the instant it reaches its maximum height.

2. Hmm...Oddly worded. It sounds like "stop and stay stopped" is supposed to mean: the object was initially moving, but then slowed to a stop, and thereafter it did not move any more. If that interpretation is correct, then the answer is "No." This is because (a) its constant acceleration is nonzero (we know this because its speed changed); and (b) a nonzero constant acceleration implies a continuous change in speed (which means it can't "stay stopped").

However, if "stop and stay stopped" does NOT imply that the object was once moving (i.e., maybe it was just ALWAYS stopped), then then answer is "Yes." This case can happen if the constant acceleration is constantly zero.

Answer 4

Let me help you out:

Rick and Lyons have it right.

The force of gravity near the earth is a force that results in constant acceleration.

If you throw a ball up in the air, it accelerates downward the entire time. Since the initial velocity is upward, the velocity vector gets smaller with time (more downward) meaning the ball comes to a stop at some point in the air. The acceleration does not change, and the velocity vector continues to point more and more downward with time. This means that the object falls to the earth, but is now speeding up. This is constant acceleration. If you throw the ball downard, it will go downward faster, if you let it go from rest, it goes downward faster, and thrown up in the air the velocity goes downward (less upward) faster with time. The answers to 1 and 2 are then:

1. Yes.

2. No.

Answer 5

1. no
when the velocity is zero then acceleration is also zero.

2. yes
if the acceleration is constant. You can stop it by reversing the acceleration until to a stop
if it is a force other than friction that cause the reverse acceleration, then the direction of motion might be reversed in opposite direction.

Answer 6

You first have been given to obtain the properly suited expression to your concern that's straightforward for the situation you have the given expression h(t) = t^3 - 9t^2 + 200 for the rate may be the 1st spinoff h'(t)=v(t)=3t^2-18t for the acceleration may be the 2d spinoff h''(t)=v'(t)=a(t)=6t-18 so there you circulate a)what's the malicious program's velocity after 2 minutes? you in basic terms could replace the time interior the properly suited expression so... v(2)=3(2)^2-18(2) remedy for the rate in 2 minutes v(2)= -24inches/minute so the rate is going down b)whilst will the malicious program substitute guidelines? it is an inflection element you will choose the 0.33 spinoff which would be h'''(t)=6 and you will choose the roots from the 2d spinoff so... h''(t)=6t-18 for this you may experience this to 0 so 6t-18=0 and the sole root would be t=3 this root gets replaced interior the 0.33 spinoff and... h'''(3)=6 which differs 0 so given this the foundation would be an inflection element, the direction substitute of your malicious program c)whilst is the malicious program's acceleration equivalent to 0? you in basic terms could experience the acceleration to 0 that's the 2d spinoff a(t)=6t-18 0=6t-18 t=3 in basic terms like interior the previous question there you circulate!

Answer 7

If a particle is at rest, it can not be accelerating. A particle not moving will have a constant acceleration of zero.

Answer 8

I'm guessing you are wondering about acceleration near the speed of light-is that right?