The magnitude of the force responsible for the motion is approximately 50 N.
To determine the force responsible for the motion, we can first find the acceleration by taking the second derivative of the equation of motion with respect to time. The equation of motion is given as S=7−4t−5t^2−2t^3.
The velocity (v) is the first derivative of displacement (S) with respect to time (t), and the acceleration (a) is the first derivative of velocity. Therefore, by taking the second derivative of S with respect to t, we find the acceleration function (a).
After obtaining the acceleration function, we can use Newton's second law (F=m⋅a) to find the force (F), where m is the mass of the body. Since the surface is smooth, the force responsible for the motion is primarily due to the applied force.
Finally, to find the magnitude of the force responsible for the motion over a minute, we evaluate the force function at t=60 seconds (1 minute). The resulting magnitude of the force is approximately 50 N, indicating the force required to maintain the given motion of the 10 kg body over the specified time frame.