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 ...
- 3,248
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.
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5
votes
Can you directly feel the effect of gravity, or only opposing forces?
You are almost completely right.
What we do not and cannot feel is a uniform gravitational force. By “uniform” here I mean in the sense of general relativity where the force of gravity is just a ...
- 109k
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
2
votes
Why is F = ma and not mv?
no, you don't have it right. If a ball ($m$) has momentum $\vec p_i$ hits you in the head, that collision takes time $\Delta t$. If the ball bounces away with momentum $\vec p_f$, then the momentum ...
- 39.5k
1
vote
Can Shear-Stress Cause Translation Motion? If Not, Why is There a Viscous Term in the Navier-Stokes Equations?
A constant/homogeneous shear stress can't, but a gradient of a shear stress can. That's why the viscous force term has a $\nabla^2$, not a $\nabla$.
- 3,178
1
vote
Can Shear-Stress Cause Translation Motion? If Not, Why is There a Viscous Term in the Navier-Stokes Equations?
An unbalanced shear load on an element causes both translation and rotation; by the parallel-axis theorem, the load can be replaced by a force acting on the center of the element plus a moment around ...
- 28.1k
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