A 20kg box is being pushed across the floor by a constant force (90,0,0)N. The coefficient of kinetic friction for the table and box is 0.25. At t=5s the box is at location ( 8,2,-1)m, traveling with velocity (3,0,0) m/s. What is the position and velocity at t=5.6s?

To find the position and velocity at t=5.6s, we need to use the given information and apply the laws of motion. Here's how you can solve the problem step by step:

Step 1: Calculate the net force acting on the box.
The net force can be calculated using the equation: net force = applied force - frictional force.
The applied force is given as (90, 0, 0) N.
The frictional force can be found using the equation: frictional force = coefficient of friction * normal force.
The normal force is equal to the weight of the box, which can be calculated as the mass times the acceleration due to gravity (9.8 m/s^2).
Therefore, the normal force is given by: normal force = mass * acceleration due to gravity.
Given that the mass of the box is 20 kg, the normal force is: normal force = 20 kg * 9.8 m/s^2.
Now, the frictional force can be calculated as: frictional force = 0.25 * (20 kg * 9.8 m/s^2).
So, the frictional force is (0.25 * (20 * 9.8), 0, 0) N.
Substituting these values into the net force equation, we get: net force = (90, 0, 0) N - (0.25 * (20 * 9.8), 0, 0) N.

Step 2: Calculate the acceleration.
The net force is equal to mass times acceleration (Newton's second law of motion).
So, we have: net force = mass * acceleration.
Dividing both sides of the equation by the mass, we find: acceleration = net force / mass.
Substituting the values we calculated, we get: acceleration = ((90, 0, 0) N - (0.25 * (20 * 9.8), 0, 0) N) / 20 kg.

Step 3: Calculate the change in position and velocity at t = 5.6s.
Since the acceleration is constant, we can use the kinematic equations to find the change in position and velocity.
The position can be found using the equation: position = initial position + initial velocity * time + 0.5 * acceleration * time^2.
The initial position is given as (8, 2, -1) m.
The initial velocity is given as (3, 0, 0) m/s.
The time is given as t = 5.6s.
Now, we can substitute these values into the position equation to calculate the position at t = 5.6s.

Similarly, the velocity can be found using the equation: velocity = initial velocity + acceleration * time.
We can substitute the given values into this equation to calculate the velocity at t = 5.6s.

By following these steps, you should be able to find the position and velocity at t=5.6s.