The displacement of a 1kg object as a function of time t in the x-y plane is giv

Question

The displacement of a 1kg object as a function of time t in the x-y plane is given by x=20t+30t^2 and y=25-30t, where x and y are in units of meters and t is in seconds.
A. The force acting on the object is
B. The magnitude and direction of the velocity of the object from the positive x axis at the end of 1 second would be
The displacement of a 1kg object as a function of time t in the x-y plane is given by x=20t+30t^2 and y=25-30t, where x and y are in units of meters and t is in seconds.
A. The force acting on the object is
B. The magnitude and direction of the velocity of the object from the positive x axis at the end of 1 second would be

A. The force acting on the object is
B. The magnitude and direction of the velocity of the object from the positive x axis at the end of 1 second would be

Explanation / Answer

A.   vx= dx/dt = 20 + 60t    => vx(1) = 80 m/s
vy = dy/dt = -30     = > vy(1) = -30 m/s

a =dvx/dt = 60 m/s2
ay =dvy/dt = 0

F = ma = 60 N

b) magnitude = sqrt(vx ^2 + vy^2) = 85.44 m/s

direction = tan-1(vy/vx)   =   - 20.56 defrees   below x-axis

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