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 can use the formula for kinetic energy:
Kinetic Energy (KE) = 1/2 * mass * velocity^2
First, let's calculate the final velocity of the body. We know the body is experiencing a constant retarding force, which means it's accelerating in the opposite direction of its initial motion. We can use Newton's second law of motion to find the acceleration:
Force (F) = mass (m) * acceleration (a)
The given force acting on the body is 10 newtons, and the mass of the body is 6 kg. Rearranging the formula, we can solve for acceleration:
acceleration (a) = Force (F) / mass (m)
a = 10 N / 6 kg
a ≈ 1.67 m/s²
Since the acceleration is constant, we can use the following kinematic equation to find the final velocity:
Final velocity (v) = Initial velocity (u) + acceleration (a) * time (t)
Given:
Initial velocity (u) = 12 m/s
Acceleration (a) = -1.67 m/s² (since it's retarding)
Time (t) = 3 seconds
v = 12 m/s + (-1.67 m/s²) * 3 s
v ≈ 12 m/s - 5 m/s
v ≈ 7 m/s
Now that we have the final velocity, we can calculate the kinetic energy using the formula mentioned earlier:
KE = 1/2 * mass * velocity^2
KE = 1/2 * 6 kg * (7 m/s)^2
KE = 1/2 * 6 kg * 49 m²/s²
KE = 147 joules
Therefore, the kinetic energy of the body at the end of 3 seconds is 147 joules.