Question

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.

Answer 1

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