Answer: (a) To determine the value of force (F) acting on the body, we can use Newton's second law of motion, which states that the force applied to an object is equal to the mass of the object multiplied by its acceleration:
F = m * a
where:
F = force (in Newtons, N)
m = mass of the body (in kilograms, kg)
a = acceleration of the body (in meters per second squared, m/s²)
Given data:
m = 5 kg (mass of the body)
Initial velocity (u) = 2 m/s
Final velocity (v) = 8 m/s
Time taken (t) = Not given, we need this information to calculate acceleration.
Acceleration (a) can be calculated using the formula:
a = (v - u) / t
Now, let's find the acceleration:
a = (8 m/s - 2 m/s) / t
We are not given the time taken (t) in the problem statement. Without knowing the time taken, we cannot determine the value of acceleration or the force applied (F).
(b) If F = 10 N, to determine the displacement of the body 6 seconds after the body starts to move from rest, we can use the equation of motion for uniformly accelerated motion:
s = ut + (1/2) * a * t^2
where:
s = displacement of the body
u = initial velocity (which is 0 m/s since the body starts from rest)
t = time (6 seconds in this case)
a = acceleration (which we will assume to be 10 N/kg, given that F = 10 N and m = 5 kg)
Now, let's calculate the displacement:
s = 0 + (1/2) * 10 N/kg * (6 s)^2
s = 0 + 0.5 * 10 N/kg * 36 s^2
s = 0 + 5 * 36 m
s = 180 m
The displacement of the body 6 seconds after starting to move from rest is 180 meters.