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Question 6: Particle motion (15 points) A particle of mass $m$ is moving along the $x$-axis with a velocity $v = v(x)$ that depends on the position $x$ according to $$v(x) = A \cosh(\beta x) = A \left(\frac{e^{\beta x} + e^{-\beta x}}{2}\right),$$(8) where $A > 0$ and $\beta$ are constants. (a) What are the physical dimensions (units) of $A$ and $\beta$? (b) Find the force $F(x)$ acting on the particle as a function of $x$, $A$ and $\beta$. Hint: use N2L in the form $F = \frac{dp}{dt} = m\frac{dv}{dt}$ and then use the chain rule. (c) Check your expression for $F(x)$ for dimensional consistency.

          Question 6: Particle motion (15 points)
A particle of mass $m$ is moving along the $x$-axis with a velocity $v = v(x)$ that depends on the position
$x$ according to
$$v(x) = A \cosh(\beta x) = A \left(\frac{e^{\beta x} + e^{-\beta x}}{2}\right),$$(8)
where $A > 0$ and $\beta$ are constants.
(a) What are the physical dimensions (units) of $A$ and $\beta$?
(b) Find the force $F(x)$ acting on the particle as a function of $x$, $A$ and $\beta$.
Hint: use N2L in the form $F = \frac{dp}{dt} = m\frac{dv}{dt}$ and then use the chain rule.
(c) Check your expression for $F(x)$ for dimensional consistency.

Question 6: Particle motion (15 points)
A particle of mass m is moving along the x-axis with a velocity v = v(x) that depends on the position
x according to

v(x) = A cosh(β x) = A ((e^β x + e^-β x)/(2)),
(8)
where A > 0 and β are constants.
(a) What are the physical dimensions (units) of A and β?
(b) Find the force F(x) acting on the particle as a function of x, A and β.
Hint: use N2L in the form F = (dp)/(dt) = m(dv)/(dt) and then use the chain rule.
(c) Check your expression for F(x) for dimensional consistency.

Added by Purificaci-N A.

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