# A 60 kg Bicyclist Going 2 m/s Increased his Work Output by 1,800 j. What was his Final Velocity? – Find Out Now!

A 60 kg bicyclist, moving at a speed of 2 m/s, experienced a significant increase in work output by an impressive 1,800 J. Now the question arises: what is the final velocity? Let’s delve into the calculations to find out.

## A 60 kg Bicyclist Going 2 m/s Increased his Work Output by 1,800 j. What was his Final Velocity?

### Calculating Initial Parameters

To understand the situation, let’s break down the initial parameters of the bicyclist. We have a 60 kg rider moving at a speed of 2 m/s. These values are crucial in determining the final velocity after an increase in work output.

The mass of the bicyclist, which is 60 kg, plays a significant role in calculating the overall energy involved in this scenario. Additionally, knowing that the cyclist is initially traveling at 2 m/s provides us with a starting point for our calculations.

### Determining the Final Velocity

With these initial parameters and understanding of the increased work output, we can now determine what the final velocity will be for our cyclist. The final velocity represents how fast they will be moving after expending extra energy.

To calculate this value accurately, we need more information about other forces acting on our rider (such as friction or air resistance). Without these details, it’s challenging to provide an exact answer without making assumptions.

However, based on conservation of mechanical energy principles and assuming no external forces significantly affect our bicyclist’s motion beyond increased work output alone, we can approximate that their final velocity will be higher than their initial speed of 2 m/s. This is because additional work input translates into greater kinetic energy and thus higher velocity.

Keep in mind that this approximation assumes ideal conditions and neglects various real-world factors. For a more precise calculation, a comprehensive understanding of the external forces acting on the bicyclist would be necessary.

## Checking Units and Converting if Necessary

To determine the final velocity of a 60 kg bicyclist who increased their work output by 1,800 J while initially traveling at a speed of 2 m/s, we need to carefully check the units involved and make any necessary conversions.

### Step 1: Identifying the Given Information

Let’s break down the given information:

• Mass of the bicyclist: 60 kg
• Initial velocity: 2 m/s
• Increase in work output: 1,800 J

### Step 2: Understanding Work and Energy

To solve this problem, we need to apply principles from physics related to work and energy. In particular, we can use the work-energy principle which states that the work done on an object is equal to the change in its kinetic energy.

The equation for calculating work is:

Work (W) = Force (F) × Distance (d) × Cosine of Angle (θ)

In this case, since angle and distance are not provided, we’ll focus on calculating changes in kinetic energy using another formula:

ΔKE = W

Where ΔKE represents the change in kinetic energy.

### Step 3: Calculating Change in Kinetic Energy

Since there are no external forces acting on our cyclist apart from his own exertion, we can assume that all of his increased work output directly contributes to changing his kinetic energy.

Using the formula ΔKE = W, we can equate it with our given increase in work output:

ΔKE = W = 1800 J

### Step 4: Applying Equations for Kinetic Energy

The equation for calculating kinetic energy is:

Kinetic Energy (KE) = (1/2) × mass × velocity^2

Let’s denote the initial velocity as v_initial and final velocity as v_final. We know that KE_initial is equal to (1/2) × mass × v_initial^2, and ΔKE is equal to KE_final minus KE_initial:

ΔKE = KE_final – KE_initial

Substituting the equations for kinetic energy, we have:

1800 J = (1/2) × 60 kg × v_final^2 – (1/2) × 60 kg × 2 m/s^2

### Step 5: Solving for Final Velocity

Now we can solve for the final velocity. Rearranging the equation, we get:

v_final^2 = (1800 J + (1/2) × 60 kg × 4 m/s^2) / (1/2) × 60 kg

Simplifying further, we have:

v_final^2 = (3600 J + 120 J) / 30 kg

Combining like terms, we get:

v_final^2 = 122 J / 30 kg

Finally, taking the square root of both sides gives us the final velocity:

v_final ≈ √(122 J / 30 kg)

After evaluating this expression using a calculator or software application, the approximate value of the final velocity will be obtained.

By carefully checking and understanding the given information and applying relevant principles from physics related to work and energy, we can calculate that the final velocity of a bicyclist weighing 60 kg who increased their work output by 1,800 J while initially traveling at a speed of 2 m/s is approximately √(122 J /30 kg).