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

Answer:

F= 172.945 N

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 = $\sqrt{3436.96}$ = 58.626 m/s²

Now F= ma = 2.95 kg × 58.626 m/s²

F= 172.945 N