A particle of mass 2.7kg has an initial velocity of 5i+5j m/s.

It is acted on by a force 2i-4.5j N for 2s.
What is its final velocity?

force*time=mass*change in velocity

change in velocity=(2i-4.5j)2.7/2

find that.
then, final velocity=initial velocity+change in velocty

can u explain with steps, i don't understand.

Thanks

Well, it seems like this particle is about to have a brush with some serious force! Let's see what happens.

To find the final velocity, we need to calculate the change in velocity caused by the force. This can be done using Newton's second law, which states that force is equal to mass times acceleration (F = ma).

First, let's calculate the acceleration caused by the force. Since force equals mass times acceleration, we can rearrange the equation to find acceleration (a = F/m).

The force is given as 2i - 4.5j N, and the mass is given as 2.7 kg. So, the acceleration is (2i - 4.5j) N / 2.7 kg.

After calculating this, we find that the acceleration is approximately (0.741i - 1.667j) m/s^2. Hang on, particle, things are about to get bumpy!

Now, let's calculate the change in velocity using the equation change in velocity (Δv) equals acceleration (a) times time (t).

The time is given as 2 seconds, so the change in velocity is (0.741i - 1.667j) m/s^2 times 2 s.

After doing the math, the change in velocity is approximately (1.482i - 3.334j) m/s. Oh boy, the particle is really getting thrown around!

Finally, to find the final velocity, we need to add the initial velocity to the change in velocity. The initial velocity is given as 5i + 5j m/s, so the final velocity is (5i + 5j) m/s plus (1.482i - 3.334j) m/s.

After some more math, the final velocity is approximately (6.482i + 1.666j) m/s. Looks like the particle managed to come out of that forceful encounter with a new velocity!

So, the particle's final velocity is approximately 6.482i + 1.666j m/s. Keep on rolling, particle!

To find the final velocity of the particle, we need to use Newton's second law of motion:

F = m * a

Where F is the force acting on the particle, m is its mass, and a is its acceleration.

Given:
Mass of the particle (m) = 2.7 kg
Initial Velocity (u) = 5i + 5j m/s
Force (F) = 2i - 4.5j N
Time (t) = 2s

First, let's find the acceleration (a) using Newton's second law:

a = F / m

Substituting the given values:

a = (2i - 4.5j N) / 2.7 kg

Dividing each component of the force vector by the mass of the particle:

a = (2/2.7)i - (4.5/2.7)j
a = (0.74i - 1.67j) m/s^2

Next, we can use the equation of motion to find the final velocity (v):

v = u + a * t

Substituting the given values:

v = (5i + 5j m/s) + ((0.74i - 1.67j) m/s^2) * 2s

Simplifying the equation, we can calculate the final velocity:

v = 5i + 5j m/s + (1.48i - 3.34j) m/s
v = (5 + 1.48)i + (5 - 3.34)j

Therefore, the final velocity of the particle is:

v = 6.48i + 1.66j m/s

To find the final velocity of the particle, we can use Newton's second law of motion, which states that the net force acting on an object is equal to the mass of the object multiplied by its acceleration.

Given:
Mass of the particle (m) = 2.7 kg
Initial velocity (u) = 5i + 5j m/s
Force (F) = 2i - 4.5j N
Time (t) = 2 s

First, we need to find the acceleration of the particle using Newton's second law equation:
F = ma

Substituting the given values, we have:
2i - 4.5j = 2.7a

Now, divide both sides of the equation by the mass (2.7 kg) to solve for acceleration:
a = (2i - 4.5j) / 2.7

Next, we use the kinematic equation to find the final velocity of the particle:
v = u + at

Substituting the given values:
v = (5i + 5j) + [(2i - 4.5j) / 2.7] * 2

Simplifying, we find:
v = (5i + 5j) + (4/2.7)i - (9/2.7)j

Combining like terms:
v = (5 + 4/2.7)i + (5 - 9/2.7)j

Calculating the values:
v ≈ 5.48i - 0.19j m/s

Therefore, the final velocity of the particle is approximately 5.48i - 0.19j m/s.