Final answer:
The speed of the 29 kg cart, after being pushed by a 20 N force over a distance of 9.3 m on a frictionless surface, is approximately 3.58 m/s as calculated from the work-energy principle.
Step-by-step explanation:
To calculate the speed of the cart after it has been pushed 9.3 m by a constant 20 N force, we can use the work-energy principle. The work done on the cart by the force is equal to the change in the cart's kinetic energy. Since the initial speed is zero (the cart starts from rest), the final kinetic energy will be equal to the work done.
Work done, W, is calculated as:
W = force × distance
W = 20 N × 9.3 m = 186 J
The kinetic energy (KE) of the cart is given by:
KE = ½ × mass × speed2
Since the work done on the cart is equal to its kinetic energy, we can set them equal and solve for speed:
186 J = ½ × 29 kg × speed2
By solving for speed, we get:
speed = √(2 × 186 J / 29 kg) = √(12.8276) ≈ 3.58 m/s
Therefore, the speed of the cart when it has been pushed 9.3 m is approximately 3.58 m/s.