A body of mass 5 kg is moving with a velocity of 10 m/s. Now a force which delivers a constant power of 75 watt is applied on it for 10s in the same direction. The velocity of body after 10s will be?

Kindly also explain, and it would be wonderful if you could glance at what I worked out and point out my flaw.

This is what I thought :

KE gained = 75 watt * 10 sec = 750J

=> momentum gained = (2m*KE)^(1/2) = (2*5*750)^(1/2) = 7500^(1/2)

Force = delta p / delta t = 50{3^(1/2)}

=> accelaration = 50{3^(1/2)} / mass = 10{3^(1/2)}

=>velocity = u + at = 10 + 10{3^(1/2)} * 10

This doesn't match any options

To find the final velocity of the body after applying a constant power for a specific duration, we can break down the problem step by step. Let's analyze the situation carefully and correct any misconceptions in your calculations.

Understanding the Problem

You have a body with a mass of 5 kg moving at an initial velocity of 10 m/s. A force is applied that delivers a constant power of 75 watts for 10 seconds. Our goal is to determine the final velocity after this time period.

Key Concepts

• Power (P) is defined as the rate at which work is done or energy is transferred. The formula is: P = F × v, where F is the force applied and v is the velocity.
• Work (W) done by the force can also be expressed in terms of power: W = P × t.
• Kinetic Energy (KE) is given by the formula: KE = 0.5 × m × v².

Calculating Work Done

First, we calculate the work done by the force over the 10 seconds:

W = P × t = 75 W × 10 s = 750 J.

Initial Kinetic Energy

Next, we find the initial kinetic energy of the body:

KE_initial = 0.5 × m × v² = 0.5 × 5 kg × (10 m/s)² = 0.5 × 5 × 100 = 250 J.

Final Kinetic Energy

The final kinetic energy after the work is done will be the initial kinetic energy plus the work done:

KE_final = KE_initial + W = 250 J + 750 J = 1000 J.

Finding Final Velocity

Now we can find the final velocity using the kinetic energy formula:

KE_final = 0.5 × m × v_final².

Substituting the values:

1000 J = 0.5 × 5 kg × v_final².

1000 = 2.5 × v_final².

v_final² = 1000 / 2.5 = 400.

v_final = √400 = 20 m/s.

Summary of Findings

The final velocity of the body after 10 seconds, when a constant power of 75 watts is applied, is 20 m/s.

Identifying the Flaw in Your Calculation

Your approach to calculating kinetic energy gained was correct, but the method you used to derive momentum and subsequently force was unnecessarily complicated. Instead of calculating momentum and then deriving acceleration, directly using the relationship between work done and kinetic energy simplifies the process significantly. By focusing on the work-energy principle, we can avoid potential errors in intermediate steps.

In summary, the final velocity after applying a constant power of 75 watts for 10 seconds is 20 m/s. This approach emphasizes the importance of understanding the relationships between power, work, and kinetic energy in solving physics problems effectively.