Here is one of my questions from my physics study. It tells me the answer (35 J), but how do I find that answer? I would appreciate a formula or step by step calculation. Thanks! :)

A 30 kg kid on rollerskates is moving 1 m/s. His brother pushes him with a force of 5 N. What will be his kinetic energy after his brother pushes him 4.0 m? (35 J)

Efinal= 1/2mvi^2+fd

Thanks! That works and makes sense. :)

To find the kinetic energy of the kid after being pushed by his brother, we can use the formula for kinetic energy:

Kinetic Energy = 0.5 * mass * velocity^2

In this case, the kid's mass is 30 kg and his initial velocity is 1 m/s. We need to find the final velocity after he is pushed by his brother.

To find the final velocity, we can use Newton's second law of motion:

Force = mass * acceleration

In this case, the force exerted by the brother is 5 N. The acceleration can be found by dividing the force by the mass:

acceleration = Force / mass

Once we know the acceleration, we can use the equations of motion to find the final velocity. Since the initial velocity is 1 m/s and the distance traveled is 4.0 m, we can use the following equation:

final velocity^2 = initial velocity^2 + 2 * acceleration * distance

Once we have the final velocity, we can substitute it into the formula for kinetic energy to find the answer.

Let's calculate step by step:

Step 1: Calculate acceleration
acceleration = Force / mass
acceleration = 5 N / 30 kg

Step 2: Calculate final velocity
final velocity^2 = initial velocity^2 + 2 * acceleration * distance
final velocity^2 = (1 m/s)^2 + 2 * (acceleration) * (4.0 m)
final velocity^2 = 1 m^2/s^2 + 2 * (5 N / 30 kg) * 4.0 m

Step 3: Simplify final velocity equation
final velocity^2 = 1 m^2/s^2 + 40 Nm / 30 kg * 4.0 m
final velocity^2 = 1 m^2/s^2 + (40 N * 4.0 m) / 30 kg
final velocity^2 = 1 m^2/s^2 + (160 Nm) / 30 kg

Step 4: Calculate final velocity
final velocity^2 = 1 m^2/s^2 + 160 Nm / 30 kg
final velocity^2 = (1 m^2/s^2 * 30 kg + 160 Nm) / 30 kg
final velocity^2 = (30 kg * 1 m^2/s^2 + 160 Nm) / 30 kg
final velocity^2 = 30 m^2/s^2 + 160 Nm / 30 kg
final velocity^2 = 30 m^2/s^2 + 5.333 m^2/s^2

final velocity^2 = 35.333 m^2/s^2

Taking the square root of both sides:

final velocity = √(35.333 m^2/s^2)
final velocity ≈ 5.95 m/s

Step 5: Calculate kinetic energy
Kinetic Energy = 0.5 * mass * velocity^2
Kinetic Energy = 0.5 * 30 kg * (5.95 m/s)^2
Kinetic Energy ≈ 0.5 * 30 kg * 35.4025 m^2/s^2
Kinetic Energy ≈ 531.0375 J

Therefore, the kinetic energy of the kid after being pushed by his brother is approximately 531.0375 J, which when rounded to the nearest whole number is 531 J.