At what speed does a 1000 kg compact car have the same kinetic energy as a 20,000 kg truck going 25 km/h?

Verified step by step guidance

1. Identify the formula for kinetic energy, which is given by KE = $\frac{1}{2}m{v}^2$, where $m$ is the mass of the object and $v$ is its velocity.
2. Calculate the kinetic energy of the truck using its mass and velocity. Substitute the mass of the truck (20,000 kg) and its velocity (25 km/h, convert this to meters per second by multiplying by $\frac{1000}{3600}$).
3. Set the kinetic energy of the car equal to the kinetic energy of the truck. This gives the equation $\frac{1}{2}(1000)v^2=\frac{1}{2}(20000){(25\times \frac{1000}{3600})}^2$.
4. Simplify the equation to solve for $v$, the velocity of the car. Cancel out the $\frac{1}{2}$ from both sides and solve for $v^2$.
5. Take the square root of both sides of the equation to find $v$, the velocity of the car in meters per second. Convert this velocity back to km/h if necessary by multiplying by $\frac{3600}{1000}$.

Key Concepts

Kinetic Energy

Kinetic energy is the energy an object possesses due to its motion, calculated using the formula KE = 1/2 mv², where m is the mass and v is the velocity. This concept is crucial for comparing the energy of different objects in motion, as it directly relates to both their mass and speed.

Mass and Velocity Relationship

The relationship between mass and velocity is fundamental in understanding how kinetic energy varies with changes in these parameters. For two objects to have the same kinetic energy, adjustments in either mass or velocity must be made, illustrating the inverse relationship between mass and the square of velocity in the kinetic energy formula.

Unit Conversion

Unit conversion is essential when dealing with different measurement systems, such as converting kilometers per hour (km/h) to meters per second (m/s). This ensures consistency in calculations, particularly when comparing the kinetic energies of objects with different masses and speeds, as accurate units are critical for correct results.