As a 2.0-kg object moves from (4.4 i + 5j) m to ( 11.6 i - 2j) m, the constant resultant force acting on it is equal to (41 - 9j) N. If the speed of the object at the initial position is 4.0 m/s,
what is its kinetic energy at its final position?

v_f = 10.38 m / s

Explanation:

For this exercise we can use the relationship between work and kinetic energy

          W = ΔK

note that the two quantities are scalars

Work is defined by the relation

          W = F. Δx

the bold are vectors.  The displacement is

          Δx = r_f -r₀

          Δx = (11.6 i - 2j) - (4.4 i + 5j)

          Δx = (7.2 i - 7 j) m

          W = (4 i - 9j). (7.2 i - 7 j)

remember that the dot product

           i.i = j.j = 1

           i.j = 0

           W = 4  7.2 + 9  7

           W = 91.8 J

the initial kinetic energy is

           Ko = ½ m vo²

           Ko = ½ 2.0 4.0²

           Ko = 16 J

we substitute in the initial equation

          W = K_f - K₀

          K_f = W + K₀

          ½ m v_f² = W + K₀

          v_f² = 2 / m (W + K₀)

          v_f² = 2/2 (91.8 + 16)

           v_f = √107.8

          v_f = 10.38 m / s

i think it’s a. this is because if they measured the mass of something with a mass of 150g, then their final answer would have to be approximately 150g. though all of their answers are almost 150, rosa and tran have the closest answers (or the exact answer) to the accurate one.

hi there!

your question asks at which segment does freezing occur.

since we're talking about water, the freezing point of water will be 32 degrees fahrenheit or below.

hope this ! ~