A body of mass 4kg is acted on by a constant force of 12N for 3 seconds. Determine the kinetic energy gained by the body at the end of the time.
F = ma
v = at
KE = 1/2 mv^2
F=ma
V= at
K.E= 1/2mv^2
==K.E = 1/2m(at)^2
=1/2ma^2t^2
=1/2ma *a*t^2
=1/2F*a*t^2
a=g
To determine the kinetic energy gained by the body, we can use the formula for kinetic energy:
Kinetic Energy (KE) = 1/2 * mass * velocity^2
Given:
Mass (m) = 4 kg
Force (F) = 12 N
Time (t) = 3 seconds
To find the final velocity, we need to use Newton's second law of motion:
Force (F) = mass (m) * acceleration (a)
Rearranging the equation, we get:
Acceleration (a) = Force (F) / mass (m)
Substituting the values, we get:
Acceleration (a) = 12 N / 4 kg = 3 m/s^2
Now, using the equation of motion:
Final velocity (v) = Initial velocity (u) + (acceleration (a) * time (t))
Assuming the initial velocity is 0 m/s, we have:
Final velocity (v) = 0 + (3 m/s^2 * 3 s) = 9 m/s
Finally, substituting the mass and final velocity values into the formula for kinetic energy, we get:
Kinetic Energy (KE) = 1/2 * 4 kg * (9 m/s)^2
= 1/2 * 4 kg * 81 m^2/s^2
= 162 J
Therefore, the kinetic energy gained by the body at the end of the time is 162 joules.
To determine the kinetic energy gained by the body, we can use the formula:
Kinetic Energy = (1/2) * mass * velocity^2
First, let's calculate the acceleration of the body using Newton's second law of motion:
Force = mass * acceleration
Rearranging the equation, we can find the acceleration:
acceleration = Force / mass
Given that the force acting on the body is 12N and the mass of the body is 4kg, we can calculate the acceleration:
acceleration = 12N / 4kg = 3 m/s^2
Now, we can calculate the final velocity of the body using the formula:
final velocity = initial velocity + acceleration * time
Since the body starts from rest, the initial velocity is 0. Therefore:
final velocity = 0 + 3 m/s^2 * 3s = 9 m/s
Now, substitute the values of mass (4kg) and the final velocity (9 m/s) into the formula for kinetic energy:
Kinetic Energy = (1/2) * 4kg * (9 m/s)^2
Calculating this, we get:
Kinetic Energy = (1/2) * 4kg * 81 m^2/s^2 = 162 J
Therefore, the kinetic energy gained by the body at the end of the time is 162 Joules.