A particle start from rest and moves with a curvilinear motionin the x-y plane.

Question

A particle start from rest and moves with a curvilinear motionin the x-y plane. The"y" component of motion is described by theequation y=7t^3meters, where t is in seconds. In the x directionthe particle maintains a constant acceleration of 12m/s^2. Find themagnitute and direction for the particle velocity and accelerationat a time on 2 seconds. Also, if the radius of the curve at 2seconds is 100 meters, find the normal acceleration componet forthe particle? I don't know if I need a graph calc to find problem. Somedirection is needed. A particle start from rest and moves with a curvilinear motionin the x-y plane. The"y" component of motion is described by theequation y=7t^3meters, where t is in seconds. In the x directionthe particle maintains a constant acceleration of 12m/s^2. Find themagnitute and direction for the particle velocity and accelerationat a time on 2 seconds. Also, if the radius of the curve at 2seconds is 100 meters, find the normal acceleration componet forthe particle? I don't know if I need a graph calc to find problem. Somedirection is needed.

Explanation / Answer

y=7t^3
and in the x dir. a=12 therefore v =12t + C and x = 6t^2 + Ct + 0 the zero is because we assume it isbeginning at the "origin"
in the y dir. y = 7t^3 v = 21 t^2 a = 42 t
now we have our two equations and since the partical is atrest C = 0.
so now just answer each of the questions for x and y
the velocity is equal to the velocity equations with 2 pluggedin for t. Once you have Vx and Vy use pythagoreantheorem....V^2=Vx^2 + Vy^2 to find V
You should get Vx = 24 and Vy = 84 Therefore V = 87.36 m/s you can also use inverse tangent to find the angle. should gettan (theta)= 84/24 so theta = 74.05
Use a similar method to find the mag and direction foracc
now for the normal acceleration. This is completely based onthe velocity. The equation is an=V^2 / R
so once you have your velocity above just square it and divideby 100. I get a value of 76.32 m/s^2
Hope this is of some help.

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