# Tagged Questions

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### What is the average velocity of the motorcycle?

The position of a person riding in a motorcycle race is give by $s(t)=4t^2+3t$, where $t$ measures time in seconds since the race began, and position is measured in feet beyond the starting line. ...
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### Curvilinear Coordinates and basis vectors

In the following notes, http://www.maths.manchester.ac.uk/~wparnell/MT20401/MT20401_lecture3.pdf $\frac{\partial \vec{r}} {\partial q_i}$ forms a basis set for the vector space. How does this happen? ...
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### Why is are these expressions in Leibniz notation not equivalent?

I have this problem, a projectile is fired into fluid with a rate of deceleration $a=-0.4v^3$ and in initial velocity $v_0=60$. We are to find how fast its going after $t=4$ seconds. If one starts ...
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### Why is this integral not returning to the original equation when derived?

A projectile is fired into fluid at a rate of $60$ (nevermind the units on this one.) It decelerates such that $a=(-.4)v^3$. This is all fine and dandy. The book provides this solution. ...
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### Mathematical modelling that involves projectile motion

I was asked to solve a mathematical differential equation to find the time taken by an object to reach the highest point and the time taken by the object to fall from its highest point to ground. I ...
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### The phase plane and potential energy

I think I have spotted a mistake in my notes, however I need help verifying my assumption: I am given the equation: $d^2s/dt^2=-s$ m=1 for simplicity I have recast it at a first order system: ...
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### Finding the centre of mass and moment of inertia about a point of a laminate

A triangular laminate OAB of uniform area density,$\rho$, has vertices at (0,0), (0,2) and (1,0). The moment of inertia about an axis through O,perpendicular to the plane of the laminate is denoted by ...
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### When finding the frequencies of normal modes, can you have a negative frequency?

Do you simply just consider the positive solutions? I tried a google search but didn't find anything quickly. The work I am studying is Lagrangian systems.
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### Using conservation of energy on inclined plane [closed]

Hello, I'm trying to solve this using conservation of energy. So for (a) KE+PE at the top = KE+PE at the bottom and then relate to energy alone plane. However, I'm unsure how to state the KE and PE ...
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### Conservation of Energy

Hello, I am trying to solve the following question using conservation of energy. Part (a) is fine, I have compared it with suvat questions and I have got: $z_{max} = v_0^2sin^2a/2g$ I am ...
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### Mechanics - A particle moving in an ellipse

A and B were fine, for C I took componentwise vectors x(t) and y(t), differentiated twice and applied $1/2mv^2$. For (d) I have no idea, and for (e) I applied: $1/2m(v_2^2-v_1^2)$; From then on, ...
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### Newtonian Mechanics - Differential equation

If we combine Newton's second law of motion i.e. $F=m\ddot{x}$ and Newton's law of gravity i.e., $$F=G\frac{mM}{x^2},$$ where $x$ is distance, we obtain the following equation: ...
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### Line Integral Problem best or easier solved using geometry?

Does anyone have any recommendation on a line integral problem involving vector fields (aka work) such that evaluating the resulting line integral using parameterization would be significantly ...
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