7. The x-coordinate of a particle in curvilinear motion is given by where x is in
meter and t is in seconds. The y-component of acceleration in meter per second squared is
given by If the particle has y-components and when
find the magnitudes of the velocity v and acceleration a when t=0.2*041 . sec
8. The y-coordinate of a particle in curvilinear motion is given by where y is
in centimeter and t is in seconds. Also, the particle has an acceleration in the x-direction
given by cm/sec2. If the velocity of the particle in the x-direction is 1.4*041cm/sec
when t=0, calculate the magnitudes of the velocity v and acceleration a of the particle when
Construct v and a in your solution. t = 1 sec.
9. A particle moves in the x-y plane with a y-component of velocity in meter per second given
by Vy =8t with t in seconds. The acceleration of the particle in the x-direction in meter per
second squared is given by ax =4twith t in seconds. When t=0, y=2m, x=0, and Vx=0. Find
the equation of the path of the particle and calculate the magnitude of the velocity v of the
particle for the instant when its x coordinate reaches 8*041m.
10.A particle moves in the X –Y plane so that its x coordinate is defined by
x = 5 t^3 – 105 t where x is in cm and t is in seconds. When t = 2 s the total acceleration is
7*041 m/s2. If the y component of acceleration is constant and the particles starts from rest at
the origin when t = 0, determine its velocity when t = 4 sec.
11.A particle moving in the x-y plane has a position vector given by where
r is in Cm and t is in seconds. Calculate the radius of curvature of the path for the position
of the particle when t=041*sec.
12.A particle starting from rest moves with the acceleration 𝑎̅ = 4𝑡𝑖̂ - 3𝑡2𝑗 - 6𝑘̂ m/s2. Determine
the principal radius of curvature of its path at t = 1.5*041 sec
13.In a certain plane motion, it is known that when the radial distance from a fixed origin is r
= 2*041cm, the r – θ components of velocity are Vr = 9*41 cm/s and Vθ = 100*041cm/s,
while the
components of acceleration are ar = - 150 cm/s2 and aθ = 250 cm/s2. At this instant, find
the angular acceleration α (i.e, alpha=theta) of the positive vector and the component of acceleration
normal to the path.
14. At the position shown in the figure, the block B is sliding outward along the straight rod
with the given values of velocity and acceleration relative to the rod simultaneously, the rod
has the given values of angular velocity ω and angular acceleration α.
Find the total acceleration of the block. What is the component of this acceleration normal
to the path described by the block?
angular velocity ω
angular acceleration α