A 4.5 object moving in two dimensions initially has a velocity = (11.5 i+ 22.0j). A net force then acts on the object for 2.0 s, after which the object's velocity is = (14.5i + 31.5j).
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To find the net force acting on the object, we can use Newton's second law of motion, which states that the net force on an object is equal to the product of its mass and acceleration.
Given:
Initial velocity, v₁ = (11.5i + 22.0j)
Final velocity, v₂ = (14.5i + 31.5j)
Time, t = 2.0 s
First, let's calculate the change in velocity (∆v):
∆v = v₂ - v₁
∆v = (14.5i + 31.5j) - (11.5i + 22.0j)
∆v = (3.0i + 9.5j)
Next, we can calculate the acceleration (a) using the equation:
a = ∆v / t
a = (3.0i + 9.5j) / 2.0 s
a = (1.5i + 4.75j) m/s²
Finally, we can calculate the net force (F) using Newton's second law:
F = m * a
Here, the mass (m) of the object is given as 4.5 kg.
F = 4.5 kg * (1.5i + 4.75j) m/s²
F = (6.75i + 21.375j) N
Therefore, the net force acting on the object is (6.75i + 21.375j) N.