Final answer:
To find the average speed of the cart for the second half of the entire time of movement, we first determine the distance and time taken for the first half of the movement. Using the equation of motion, we find the acceleration to be 50/S m/s². The average speed for the second half of the movement is 5 m/s.
Step-by-step explanation:
To find the average speed of the cart for the second half of the entire time of movement, we need to first determine the distance and time taken for the first half of the movement. In the first half, the cart starts from rest and gains a speed of 10 m/s, covering a distance S. Since the cart is moving with constant acceleration, we can use the equation of motion: v^2 = u^2 + 2as, where v is the final velocity, u is the initial velocity, a is the acceleration, and s is the distance traveled.
Using this equation, we have (10 m/s)^2 = (0 m/s)^2 + 2aS. Simplifying, we get 100 m^2/s^2 = 2aS. Rearranging the equation, we find a = 50/S m/s^2.
Now, for the second half of the movement, the cart continues with a uniform speed of υ = 10 m/s and covers the same distance S. The time taken for the second half is given by t = S/υ.
The average speed for the second half of the movement is equal to the total distance covered in the second half divided by the total time taken for the second half. The total distance covered in the second half is S, and the total time taken is 2t = 2(S/υ) = 2S/10 = S/5. Therefore, the average speed is S divided by S/5, which is equal to 5 m/s.