Final answer:
The resistance to the motion of the 30kg cart is 8N. When the applied force is increased to 14N, the cart accelerates at 0.2 m/s², since the net force acting on the cart is 6N.
Step-by-step explanation:
When a 30kg cart is pushed along a horizontal path with a constant velocity by an 8N force, this means that the resistance to the motion of the cart, which includes friction and air resistance, equals the applied force. Therefore, the resistance to motion (a) is 8N.
When the force is increased to 14N, the cart will start to accelerate because the applied force is greater than the resistance.
To calculate the acceleration (b), we use Newton's second law,
F = ma.
The net force is equal to the difference between the applied force and the resistance to motion, which is
14N - 8N = 6N.
Now, we can solve for acceleration 'a' using the equation
a = F/m,
where F is the net force, and m is the mass of the cart.
The acceleration 'a' is then
6N / 30kg = 0.2 m/s².