Suppose that the carriage's actual speed at point D was 15 m/s (or 54 km/h).Calculate its kinetic energy in joules

1. Break Down the Problem

To calculate the kinetic energy (KE) of an object, we need to know its mass and its speed. We will assume a mass for this calculation since it wasn't provided.

2. Relevant Concepts

The formula for kinetic energy is given by:

$KE = \frac{1}{2} m v^2$

where:

• $KE$ is the kinetic energy,
• $m$ is the mass of the object (in kilograms),
• $v$ is the speed of the object (in meters per second).

3. Analysis and Detail

Let’s assume the mass of the carriage is $m$ kilograms (as an example, assume $m = 1000$ kg). The speed $v$ at point D is given as 15 m/s.

Using the formula: $KE = \frac{1}{2} m v^2$

Substituting the values we have: $KE = \frac{1}{2} \times 1000 \, \text{kg} \times (15 \, \text{m/s})^2$ $KE = \frac{1}{2} \times 1000 \times 225$ $KE = 500 \times 225$ $KE = 112500 \, \text{J}$

4. Verify and Summarize

We found the kinetic energy for a mass of 1000 kg at a speed of 15 m/s to be $112500 \, \text{J}$. The actual mass of the carriage will change the final result. You would just replace $1000$ kg with the actual mass in the formula above to find the kinetic energy.

Final Answer

Assuming a mass of 1000 kg, the kinetic energy of the carriage at point D is $112500 \, \text{J}$.