a man of 1kg is acted upon a single force Fvector=(4i+4j)N.Due to force, mass is (D,0) to(1m,1m).If initially the speed of the particle 2m/s.Its final speed showd approximately be ?
4.5m/s
(A).6m/s(B).4.5m/s(C).8m/s(D).7.2m/s
To find the final speed of the particle, we need to calculate the work done on the particle by the force and use that to determine the change in kinetic energy.
1. Calculate the work done:
The work done on an object is given by the equation:
Work = Force * Displacement * cos(θ)
where θ is the angle between the force and the displacement.
In this case, the force vector is F = 4i + 4j N, and the displacement vector is D = (1 - 0)i + (1 - 0)j = i + j m.
So, the work done is:
Work = (4i + 4j) * (i + j) * cos(θ)
= 4i * i + 4i * j + 4j * i + 4j * j
= 4 + 4 + 4 + 4 (since i * i = j * j = 1 and i * j = j * i = 0)
= 16 J
2. Calculate the change in kinetic energy:
The work done on an object is equal to the change in kinetic energy. So, we can set:
Work = Change in Kinetic Energy
The initial kinetic energy is given by:
Initial Kinetic Energy = (1/2) * (mass) * (initial speed)^2
Given that the mass of the object is 1 kg and the initial speed is 2 m/s, we have:
Initial Kinetic Energy = (1/2) * 1 * 2^2 = 2 J
The final kinetic energy is equal to the sum of the initial kinetic energy and the work done:
Final Kinetic Energy = Initial Kinetic Energy + Work
= 2 + 16 = 18 J
3. Calculate the final speed:
The final speed of the particle can be found using the equation:
Final Speed = sqrt((2 * Final Kinetic Energy) / mass)
Substituting the values, we get:
Final Speed = sqrt((2 * 18) / 1)
= sqrt(36)
= 6 m/s
Therefore, the final speed of the particle is approximately 6 m/s.