The displacement of a particle with a mass of 325 g depends on time and is described by the function
x(t) = -6.0t3 + 4.0t2 - 13. All
constants are in SI units. Calculate the resultant force acting on the particle at time 2.3 s.
To find the resultant force acting on the particle at time 2.3 s, we first need to calculate the acceleration of the particle at that time by taking the second derivative of the displacement function with respect to time.
x(t) = -6.0t^3 + 4.0t^2 - 13
v(t) = dx(t)/dt = -18.0t^2 + 8.0t
a(t) = dv(t)/dt = -36.0t + 8.0
Now, we can find the acceleration of the particle at time t = 2.3 s:
a(2.3) = -36.0(2.3) + 8.0 = -82.8 m/s^2
Next, we can calculate the resultant force acting on the particle using Newton's second law:
F = ma
F = (0.325 kg) * (-82.8 m/s^2)
F = -26.82 N
Therefore, the resultant force acting on the particle at time 2.3 s is -26.82 N.