Assignment-1 Dynamics: Rectilinear and Curvilinear Motions

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Assignment 1_sem1_2018_Rectilinear and Curvilinear Motions
Due date: 28/02/2018
QUESTION 1
The motion of a particle is defined by the relation x  6t 4  2t 3  12t 2  3t  3 where x and t
are expressed in meters and seconds respectively. Determine the time, position and
velocity when the acceleration is zero (0).
QUESTION 2
A roller coaster shown in figure 1 travels along a vertical parabolic path defined by the
y
1 2
x . At point B, it has a speed of 25 m/s, which is increasing at the rate of 3 m/s2.
100
Find the following:
2.1 radius of curvature
2.2 total magnitude of the roller coaster’s acceleration when it is at point B.
Figure 1
QUESTION 3
The collar shown in Figure 2 slides along a rod OB. The angular position of the rod is
2
given by  =  2 rad, and the distance of the collar from O varies as  = 450 4 +
3
100 mm, where time  is measured in seconds. Determine the following at instant  =
0.5 s:
1.2 components of velocity, magnitude of the total velocity of the collar and its
direction relative to the rod clearly shown on the sketch.
1.3 components of acceleration, magnitude of the total acceleration of the collar
and its direction relative to the rod clearly shown on the sketch.
Figure 2
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