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.
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To find the kinetic energy of the body at the end of the time, we need to calculate its final velocity and then use the formula for kinetic energy.
The formula for calculating final velocity with constant acceleration is:
v = u + at
Where:
v = Final velocity
u = Initial velocity
a = Acceleration
t = Time
Given:
u = 12 m/s (Initial velocity)
a = F/m = 10 N/6 kg = 5/3 m/s^2 (Acceleration)
t = 3 s (Time)
Let's calculate the final velocity first using the formula:
v = u + at
v = 12 m/s + (5/3 m/s^2)(3 s)
v = 12 m/s + 5 m/s
v = 17 m/s
Now that we have the final velocity (v), we can calculate the kinetic energy (K.E.) using the formula:
K.E. = (1/2)mv^2
Where:
m = Mass
v = Final velocity
Given:
m = 6 kg (Mass)
v = 17 m/s (Final velocity)
Let's substitute these values into the formula to find the kinetic energy:
K.E. = (1/2)(6 kg)(17 m/s)^2
K.E. = (1/2)(6 kg)(289 m^2/s^2)
K.E. = (3 kg)(289 m^2/s^2)
K.E. = 867 J
Therefore, the kinetic energy of the body at the end of 3 seconds is 867 Joules.
To find the kinetic energy of the body at the end of the given time, you can use the equation:
Kinetic Energy = (1/2) * mass * velocity^2
First, let's find the final velocity of the body.
We know that the body is experiencing a constant retarding force, which means that the net force acting on it is equal to mass times acceleration (F = m * a).
The acceleration can be calculated using Newton's second law of motion (F = m * a), where F is the force and m is the mass of the body.
So, rearranging the equation, we have:
a = F / m
Plugging in the given values, we get:
a = 10 N / 6 kg
a = 1.67 m/s^2
Now, let's calculate the change in velocity (Δv) using the formula:
Δv = a * t
Plugging in the values:
Δv = 1.67 m/s^2 * 3 s
Δv = 5 m/s
The final velocity (v) can be found by subtracting the change in velocity from the initial velocity:
v = initial velocity - Δv
v = 12 m/s - 5 m/s
v = 7 m/s
Now that we have the final velocity, we can calculate the kinetic energy:
Kinetic Energy = (1/2) * mass * velocity^2
Plugging in the values:
Kinetic Energy = (1/2) * 6 kg * (7 m/s)^2
Kinetic Energy = 147 Joules
Therefore, the kinetic energy of the body at the end of the given time is 147 Joules.