A body of mass 6kg, initially moving with speed 12m/s, experiences a constant retarding force of 10 newtons for 3 seconds. Find the kinetic energy of the body at the end of this time.
To find the kinetic energy of the body at the end of the given time, we first need to determine the final velocity of the body.
Given:
Mass of the body, m = 6 kg
Initial velocity, u = 12 m/s
Retarding force, F = 10 N
Time, t = 3 s
To find the final velocity, we can use Newton's second law of motion, which states that the net force acting on an object is equal to the product of its mass and acceleration:
F = m * a
Rearranging the equation, we have:
a = F / m
Substituting the given values, we get:
a = 10 N / 6 kg
a = 1.67 m/s^2
Now, using the equation of motion, we can find the final velocity (v) using the initial velocity (u), acceleration (a), and time (t):
v = u + at
Substituting the given values, we get:
v = 12 m/s + (1.67 m/s^2) * 3 s
v = 12 m/s + 5.01 m/s
v = 17.01 m/s
Finally, we can find the kinetic energy (K.E.) of the body using the formula:
K.E. = (1/2) * m * v^2
Substituting the given values, we get:
K.E. = (1/2) * 6 kg * (17.01 m/s)^2
K.E. = 0.5 * 6 kg * (289.1401 m^2/s^2)
K.E. = 867.4203 J
Therefore, the kinetic energy of the body at the end of 3 seconds is 867.4203 Joules.