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.
How’s it solve
To find the kinetic energy of the body at the end of the given time, we first need to calculate the deceleration experienced by the body using Newton's second law.
The formula for Newton's second law is F = ma, where F is the force, m is the mass, and a is the acceleration.
Given:
Mass of the body, m = 6 kg
Force acting on the body, F = 10 N
Using Newton's second law, we can rearrange the formula to find the acceleration:
a = F/m
a = 10 N / 6 kg
a = 1.67 m/s² (approx)
Now, we can use the equation for acceleration to calculate the change in velocity over the given time period:
Δv = a × t
Δv = 1.67 m/s² × 3 s
Δv = 5.01 m/s
Since the force exerted is in the opposite direction to the initial velocity, the velocity decreases by 5.01 m/s.
To find the final velocity, we subtract the change in velocity from the initial velocity:
Final velocity = Initial velocity - Change in velocity
Final velocity = 12 m/s - 5.01 m/s
Final velocity = 6.99 m/s (approx)
Kinetic energy is given by the formula:
KE = (1/2) × m × v²
Plugging in the values:
KE = (1/2) × 6 kg × (6.99 m/s)²
KE = (1/2) × 6 kg × 48.7201 m²/s²
KE = 146.1603 J (to 4 decimal places)
Therefore, the kinetic energy of the body at the end of 3 seconds is approximately 146.1603 Joules.
To find the kinetic energy of the body at the end of the given time, we need to use the formula for kinetic energy:
Kinetic Energy (KE) = 1/2 * mass * velocity^2
Given:
Mass (m) = 6 kg
Initial velocity (u) = 12 m/s
Retarding force (F) = 10 N
Time (t) = 3 s
To determine the final velocity (v) of the body, we can use Newton's second law of motion:
Force (F) = mass (m) * acceleration (a)
Since the body is experiencing a retarding force, the acceleration will be negative:
F = ma
-10 N = 6 kg * a
a = -10 N / 6 kg
a = -5/3 m/s^2
We can now calculate the final velocity using the equation of motion:
v = u + at
v = 12 m/s + (-5/3 m/s^2) * 3 s
v = 12 m/s - 15/3 m/s
v = 7 m/s
Now that we have the final velocity, we can substitute the values into the kinetic energy formula:
KE = 1/2 * m * v^2
KE = 1/2 * 6 kg * (7 m/s)^2
KE = 1/2 * 6 kg * 49 m^2/s^2
KE = 147 J
Therefore, the kinetic energy of the body at the end of 3 seconds is 147 Joules.