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Pushing something on a theoretically frictionless surface

While you are applying the force the object will undergo acceleration $$\boldsymbol a = \frac{\boldsymbol F}{m}.$$ If the force stops acting on the object after time $t_{0}$...
• 856
Accepted

How many equations of motion? The higher order derivatives are highly correlated

The plots indicate that higher order derivatives aren't providing any real additional information — and you probably cannot trust the 3rd and higher ones too much either, given the low granularity of ...
• 11.8k
Accepted

• 4,461

The value of $g$ in free fall motion on earth

It means the speed of the falling body increases with 9.8 m/s each second.
• 1,379
1 vote

• 78.1k
1 vote

Faster Small Tires vs Slower Large Tires

Long distance trucks use large tires in part because of rolling resistance, as @AgniusVasiliauskas pointed out. But also a large tire has a more gentle curvature. This means a larger contact patch. ...
• 27.2k
1 vote

Is this $x$-$t$ graph possible? Is the distance decreasing over time in this graph?

Your “impossible” graph shows distance, while your counterexample shows the vector displacement relative to some origin. Think about a car with an odometer and a GPS. You can make your total vector ...
• 71.8k
1 vote

What's the difference between using $a=(v2-v1)/t$ and $s=u\cdot t+1/2\cdot a\cdot t^2$?

this is because v is not equal to s/t. otherwise the equation of kinematic would be s=vt not s=ut+1/2 a t^2. you cant apply speed= distance/time unless you have constant acceleration
1 vote

Finding motorcycle turning radius based on lean angle

The explanation by @user121330 uses arguments in the non-inertial frame of the rider. That'll work but I feel it is an overly complicated way to do it. Here is how you work it out in a simpler, ...
• 1,049
1 vote
Accepted

Why is instantaneous velocity tangent to trajectory?

The answer is in the definition of instantaneous velocity. While moving along a path a small change in position ${\rm d}\vec{r}$ over a small time frame ${\rm d}t$ the instantaneous velocity is ...
• 2,667
1 vote
Accepted

What direction should i exactly put for negative displacements?

Displacement is a vector. A vector has a direction, not a sign. It is frequently convenient to choose a coordinate system where vectors to the east are represented with positive numbers and vectors to ...
• 71.8k
1 vote
Accepted

Finding the time period under variable acceleration

You know that the tangential acceleration $Rd\omega/dt=\omega ^2 R$. So now you can integrate twice and find $\theta(t)$.
• 154
1 vote

Can we have motion in systems where inertia is neglected?

We sometimes assume a body has negligible mass, such as a rope in a pulley system where the pulley and weights on the ends of the rope have much greater mass than the light rope. This simplifies the ...
• 6,551
1 vote

Can we have motion in systems where inertia is neglected?

It is not clear what is meant by inertia is neglected: Small/huge inertia It could be that the inertia is so small, that particle experience huge acceleration. We do often use this kind of an ...
• 39.3k
1 vote

How to create the function of an arrow being shot?

$$x=u_{x}t$$ $$y= u_{y}t + \frac{1}{2}at^2$$ Rearranging: $$\frac{x}{u_{x}} = t$$ Substituting into y: $$y= u_{y}\left(\frac{x}{u_{x}}\right) + \frac{1}{2}a\left(\frac{x}{u_{x}}\right)^2$$ If we want ...
• 4,461
1 vote
Accepted

Initial velocity of a body when the distance travelled by it in the last second before reaching its maximum height is $5\ \textrm{m}$

The question has either an infinite number of answers, or no answer. It's convenient to follow the motion for the one second AFTER the ball reaches the peak of its trajectory. (Or run time backwards ...
• 10.4k
1 vote

Initial velocity of a body when the distance travelled by it in the last second before reaching its maximum height is $5\ \textrm{m}$

Assume that the velocity of the body right before the last second starts is V. It decreases to zero in 1s with an acceleration of g, about $10m/s^2$. So, V must be 10 m/s. Alo, the time to drop from ...
• 6,568
1 vote

How he came from the term: $L^2 - X^2 + 2Xdx = Y^2 + 2Y dy$ to $X dx = Y dy$? furthermore, how does the term $(X/Y)dx/dt = dy/dt = v'$?

The eq relating the values is $$x^2 + y^2 = L^2$$ Implicitly differentiating with respect to time. $$2x \frac{dx}{dt} + 2y \frac{dy}{dt} = 0$$ Rearranging,  \frac{dy}{dt} = -\frac{x}{y} \frac{dx}{dt}...
• 4,461
1 vote

Determine the meaning of a gradient of a graph

It really depends on the specific situation. The general meaning of gradient is the spatial rate of change in a quantity. For example in a temperature field $T(x,y)$, the gradient $\vec {\nabla T}$ ...
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