Final answer:
To determine the final velocity of the cart, we can use the equation: Final velocity = Initial velocity + (Acceleration * Time). In this case, the initial velocity is 0 m/s (since the cart is starting from rest), the acceleration is 6.00 m/s² south, and the time is unknown. However, we know that the cart has a displacement of 630 m south. Using the formula for displacement and solving for time, we find that the time taken is 17.67 seconds. Finally, substituting the values into the final velocity equation, we find that the final velocity of the cart is 106.02 m/s south.
Step-by-step explanation:
To determine the final velocity of the cart, we can use the equation:
Final velocity = Initial velocity + (Acceleration * Time)
In this case, the initial velocity is 0 m/s (since the cart is starting from rest), the acceleration is 6.00 m/s² south, and the time is unknown. However, we know that the cart has a displacement of 630 m south.
Using the formula:
Displacement = Initial velocity * Time + 0.5 * Acceleration * Time^2
and substituting the known values:
630 m = 0 * Time + 0.5 * 6.00 m/s² * Time^2
Simplifying the equation gives us:
3.00 m/s² * Time^2 = 630 m
Solving for Time:
Time = sqrt(630 m / 3.00 m/s²)
Time = 17.67 seconds
Finally, we can calculate the final velocity using the equation:
Final velocity = 0 + (6.00 m/s² * 17.67 s)
Final velocity = 106.02 m/s south.