A particle of mass 2 kg has an initial velocity of (4.5i + 3.5j) m/s.
It is acted on by a force (5i -2j) N for 2 s.
What is its final velocity?
To find the final velocity of the particle, we need to use Newton's second law of motion, which states that the net force (F) acting on an object is equal to the mass (m) of the object multiplied by its acceleration (a).
First, we need to calculate the acceleration of the particle using the formula:
a = F / m
Given that the force acting on the particle is (5i - 2j) N and the mass of the particle is 2 kg, we can substitute these values into the formula:
a = (5i - 2j) N / 2 kg
Next, we need to determine the change in velocity (Δv) of the particle during the 2-second time interval. This can be calculated using the formula:
Δv = a * t
where "t" represents the time interval. Given that the time interval is 2 seconds, we can substitute the values into the formula:
Δv = (5i - 2j) N / 2 kg * 2 s
Now, we can calculate the change in velocity:
Δv = (5i - 2j) N / 2 kg * 2 s
Simplifying the equation, we get:
Δv = (5i - 2j) N / 2 kg * 2 s
= (5i - 2j) N / kg * s
= (2.5i - j) m/s
The change in velocity of the particle during the 2-second time interval is (2.5i - j) m/s.
Finally, to find the final velocity, we need to add the change in velocity to the initial velocity of the particle. Given that the initial velocity is (4.5i + 3.5j) m/s, we can add the two vectors together:
Final velocity = Initial velocity + Change in velocity
= (4.5i + 3.5j) m/s + (2.5i - j) m/s
= (4.5i + 2.5i) m/s + (3.5j - j) m/s
= 7i m/s + 2.5j m/s
Therefore, the final velocity of the particle is (7i + 2.5j) m/s.
F*time=m*deltaV=m(Vf-Vi)
Vf=force * time/mass + Vi
Vf=(4.5i+3.5j) *time/mass + 4.5i+3.5j
so do the math, gather like terms in i,j