26
votes
Is it ever possible that the object is moving with a velocity such that its rate of change of speed is not constant but acceleration is constant?
Hint: In the projectile motion (without drag) the acceleration $\vec{a}=\frac{d\vec{v}}{dt}$ is constant. However $\frac{d|\vec{v}|}{dt}$ is not constant, since it is negative when the projectile is ...
- 213k
9
votes
Is it ever possible that the object is moving with a velocity such that its rate of change of speed is not constant but acceleration is constant?
Prelude - a (hopefully) fun but counterintuitive geometrical fact
A nice fact which may be a bit counterintuitive, is that if you have a square with diagonal length $\ell$ and this length varies in ...
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6
votes
Is there a curve such that a ball rolling down it has constant velocity?
Lorenz'z answer is the correct one if the only force operating on the ball is gravity. If you add friction then there will instead be a 'curve' consisting a path of constant slope.
The only way to get ...
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6
votes
Accepted
Is there a curve such that a ball rolling down it has constant velocity?
There is only the constant curve. This is because energy is conserved
$$E = E_{\text{kinetic}} + E_{\text{potential}} = \text{const}.$$
so any curve that a ball rolls down (i.e. not a constant curve) ...
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6
votes
Is it ever possible that the object is moving with a velocity such that its rate of change of speed is not constant but acceleration is constant?
Yes, this happens all the time. Fire a gun, or throw a ball, or do just about anything that involves making something move. And ignore things like air resistance, curvature of the earth and so on.
...
5
votes
Limit of relative speed
Indeed this is one of the most widely answered basic question, but in the domain of answers, there's always room for improvement.
So wikipedia covers this in its Loedel Diagram section on Minkowski ...
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3
votes
Accepted
Validity of the velocity addition formulae in Special Relativity using the four-velocity
As @Prahar noted in the comments, there's no problem defining a four velocity for light. The resulting four vector however will be a light-like four vector, so it won't have the same normalization as ...
- 3,238
3
votes
Is it ever possible that the object is moving with a velocity such that its rate of change of speed is not constant but acceleration is constant?
In general if $v$ denotes the velocity, the rate of change of speed is
\begin{align*}\frac{\text{d}|v|}{\text{d}t} &= \frac{\text{d}}{\text{d}t} \sqrt{ \left< v, v \right> } \\&= \frac{1}...
- 131
3
votes
Accepted
Need help in understanding Tangential Acceleration
Derivatives speak to the instantaneous behavior at a point. It is possible to have a 1st derivative that is non-zero and a 2nd derivative that is 0 at a point. They're simply measuring two different ...
- 51.7k
1
vote
Is there a curve such that a ball rolling down it has constant velocity?
Without friction, the curve is a horizontal line.
- 1,865
1
vote
Is there a curve such that a ball rolling down it has constant velocity?
This depends on the amount of friction you have.
you need to adjust the slope such that the friction forces $F_\text{fric}$ force cancels the slope downforce $F_\text{slope}$ at the desired velocity.
...
- 1,088
1
vote
Validity of the velocity addition formulae in Special Relativity using the four-velocity
Let us start with a massive particle that moves with uniform velocity v in the lab frame. You can pick two events that the particle passes through and calculate the four velocity from them.
You know ...
- 45.6k
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