18-07-2013, 04:28 PM
Mathematics for Physics 3: Dynamics – Worksheet 2
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Preparation problems
You are expected to do the following questions before your tutorial workshop, as a preparation.
Consulting friends as well as the course team is encouraged.
Workshop problems
You are expected to do the following questions during the tutorial workshop.
Consulting friends as well as the course team is encouraged.
1. One-dimensional motion: At time t = 0 a particle of mass m is projected from the origin along the x axis
with velocity v0 > 0. The motion is resisted by friction: the force acts against the motion with magnitude of
mk|v| (k is a positive constant).
B. Write down the equation of motion above as a differential equation for v(t) and solve it taking into account
the initial condition. Sketch the functional form of the solution for the velocity as a function of time.
A. Show that the acceleration of a particle can be expressed as x
̈=
C. Integrate your result in B to obtain x(t) subject to the initial condition. Sketch the functional form of the
solution for the position as a function of time.
D. Using your results for B and C, obtain the functional relation between the position and the velocity x(v)
and sketch its functional form.
E. Write down the equation of motion above as a differential equation for v(x) and solve it taking into account
the initial condition. Verify that your result is consistent with what you got above.