Final answer:
To determine the speed of the car at a displacement of 10m when starting from rest, we need to find the net force on the car and use Newton's second law of motion. By calculating the acceleration and using equations of motion, we can find that the speed of the car is approximately 4.47 m/s.
Step-by-step explanation:
To determine the speed of the car at a displacement of 10m, we need to find the net force on the car and use Newton's second law of motion. The net force is the force exerted by the winch minus the force of friction. Since the car is starting from rest, we can set the initial velocity to 0. Using the equation F = ma, where F is the net force, m is the mass of the car, and a is the acceleration, we can solve for a by rearranging the equation to a = F/m.
Substituting the given force equation T = 100(s+1)N and the mass of the car being 2 Mg (2 * 1000 kg), we get a = 100(s+1)/(2*1000). Plugging in s = 10m, we find a = 1m/s^2. With the acceleration, we can now calculate the final velocity using the equation v = u + at, where u is the initial velocity (which is 0), a is the acceleration, and t is the time taken. Since we only have the initial and final displacement, we need to find the time taken by using the equation s = ut + 0.5at^2 and rearranging it to t = sqrt(2s/a).
Plugging in the values, we find t = sqrt(2*10/1) = sqrt(20) = 4.47s. Finally, plugging this value into the velocity equation, v = 0 + 1*4.47, we find the speed of the car at a displacement of 10m to be approximately 4.47 m/s.