Final answer:
The net horizontal force on the mass at t = 0s is 0N. At t = 1s, the net horizontal force can be determined by plugging t = 1 into the position function, and then using the derivative of the position function to find the velocity and acceleration. Finally, Newton's second law can be used to find the net horizontal force.
Step-by-step explanation:
The net horizontal force acting on an object can be found by taking the derivative of its position function with respect to time. In this case, the position function is given as x = 2t^3 - 3t^2, where t is in seconds.
To find the net horizontal force at t = 0s, we need to take the derivative of x with respect to t. The derivative of x(t) with respect to t gives us the velocity function v(t). Taking the derivative of v(t) with respect to t gives us the acceleration function a(t). Then, we can use Newton's second law (F = ma) to find the net horizontal force.
At t = 0s, the position function becomes x = 0. Plugging this into the position function, we get the equation 0 = 2(0)^3 - 3(0)^2. Therefore, at t = 0s, the net horizontal force on the mass is 0N.
At t = 1s, we can plug t = 1 into the position function to find the position of the mass at that time. Then, we can take the derivative of the position function to find the velocity and acceleration at t = 1s. Finally, we can use Newton's second law to find the net horizontal force at t = 1s.