Step-by-step explanation:
To find the magnitude of the force responsible for the motion of the body, we need to differentiate the equation of motion with respect to time (t). Let's first differentiate the given equation:
S=7-4t+5t^2 - 2t^3
Differentiating S with respect to t will give us the velocity (v):
v = ds/dt = -4+10t - 6t^2
Next, we differentiate v with respect to t to find the acceleration (a):
a = dv/dt = 10 - 12t
Now, we can use Newton's second law of motion, which states that force (F) is equal to mass (m) multiplied by acceleration (a):
F=m* a
Given that the mass (m) of the body is 10 kg, we can substitute the value of a into the equation:
F = 10* (10 - 12t)
To find the magnitude of force responsible for the motion over a minute, we need to substitute t = 60 seconds into the equation:
F= 10* (10-12 * 60) = 10* (10 - 720) = 10*(-710) =-7100 N
Therefore, the magnitude of the force responsible for the motion over a minute is 7100 N.
Hope this helps you