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A 2.95-kg object is moving in a plane, with its x and y coordinates given by x = 8t2 − 4 and y = 4t3 + 6, where x and y are in meters and t is in seconds. Find the magnitude of the net force acting on this object at t = 2.35 s.

User ApathyBear
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1 Answer

4 votes

Answer:

F= 172.945 N

Step-by-step explanation:

x = 8t² − 4

dx/dt = vx= 16 t (taking time derivative)

dv/dt = ax = 16 ( again taking derivative)

y = 4t³ + 6

dy/dt = vy= 12 t²

dy/dt = ay = 24 t (t= 2.35 s given)

acceleration a =
\sqrt{ax^(2) + ay^(2) =
\sqrt{(16^(2) + (24x2.35)^(2)}

a =
√(3436.96) = 58.626 m/s²

Now F= ma = 2.95 kg × 58.626 m/s²

F= 172.945 N

User TonyW
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