A 3 kg mass moves in a plane with its x and y coordinates given by x=5t2-1 and y

Question

A 3 kg mass moves in a plane with its x and y coordinates given by x=5t2-1 and y=3t3+2, where x and y are in meters and t is in seconds. Find the magnitude of the force acting on this mass at t=2 s. A 3 kg mass moves in a plane with its x and y coordinates given by x=5t2-1 and y=3t3+2, where x and y are in meters and t is in seconds. Find the magnitude of the force acting on this mass at t=2 s. A 3 kg mass moves in a plane with its x and y coordinates given by x=5t2-1 and y=3t3+2, where x and y are in meters and t is in seconds. Find the magnitude of the force acting on this mass at t=2 s.

Explanation / Answer

x= 5t^2-2
Vx = dx/dt = 10t
ax = dVx/dt = 10
at t= 2s, ax = 10 m/s^2

y=3t^3+2
Vy = dy/dt = 9t^2
ay = dVy/dt = 18t
at t= 2s, ay = 18*2 = 36 m/s^2

Net accleration, a = sqrt (ax^2+ay^2)
a = sqrt (10^2+36^2)
= 37.36 m/s^2

Force = m*a
=3*37.36
=112 N

Answer: 112 N

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