ES203 – Dynamics of Rigid Bodies
Problem Set #1_Midterms
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Give completely what is asked.
1. The motion of a particle is defined by the relation 𝑥 = 2𝑡 3 − 15𝑡 2 + 24𝑡 + 4, where x
and t are expressed in meters and seconds, respectively. Determine (a) when the
velocity is zero, (b) the position and the total distance traveled when the acceleration
is zero.
2. The acceleration of a particle is defined by the relation 𝑎 = −60𝑥 −1.5, where a and x
are expressed in m/s2 and meters, respectively. Knowing that the particle starts with
no initial velocity at x = 4 m, determine the velocity of the particle when (a) x = 2 m, (b)
x = 1 m, (c) x = 100 mm.
3. A projectile enters a resisting medium at x = 0 with an initial velocity v0 = 900 ft/s and
travels 4 in. before coming to rest. Assuming that the velocity of the projectile is
defined by the relation v = v0 - kx, where v is expressed in ft/s and x is in feet, determine
(a) the initial acceleration of the projectile, (b) the time required for the projectile to
penetrate 3.9 in. into the resisting medium.