Final answer:
The value of the force on a 2 kg particle that changes its velocity from 15 m/s to 35 m/s while covering a displacement of 50 m is 40 N.
Step-by-step explanation:
To calculate the force on a particle of mass 2 kg which changes velocity from 15 m/s to 35 m/s over a displacement of 50 m, we can use the work-energy principle. This principle states that the work done by a force on an object is equal to the change in the object's kinetic energy.
The change in kinetic energy (ΔKE) can be calculated using the formula:
ΔKE = ½ m v_f^2 - ½ m v_i^2
where m is the mass of the particle, v_f is the final velocity, and v_i is the initial velocity. Plugging in the given values:
ΔKE = ½ (2 kg)(35 m/s)^2 - ½ (2 kg)(15 m/s)^2
ΔKE = 2(1225) - 2(225)
ΔKE = 2450 - 450
ΔKE = 2000 J
The work done (W) is also given by the force (F) times the displacement (d):
W = F × d
Since the work done is equal to the change in kinetic energy, we have:
2000 J = F × 50 m
Therefore, the force is:
F = 2000 J / 50 m
F = 40 N
The value of the force on the particle is 40 N.