If a car's speed is increased from 30 m/s to 60 m/s, how does the kinetic energy change? A) Changes from 900 J to 1800 J B) Changes from 450 J to 900 J C) Changes from 1350 J to 54... If a car's speed is increased from 30 m/s to 60 m/s, how does the kinetic energy change? A) Changes from 900 J to 1800 J B) Changes from 450 J to 900 J C) Changes from 1350 J to 5400 J D) Changes from 900 J to 3600 J
Understand the Problem
The question is asking how the kinetic energy of a car changes when its speed is increased from 30 m/s to 60 m/s. Kinetic energy is calculated using the formula KE = 0.5 * m * v^2, where m is the mass of the car and v is its speed. The task is to calculate the initial and final kinetic energy and determine the correct change from the provided options.
Answer
The change in kinetic energy is $1350m$.
Answer for screen readers
The change in kinetic energy is $1350m$.
Steps to Solve
- Identify the initial and final speeds
The initial speed $v_1$ is given as 30 m/s. The final speed $v_2$ is 60 m/s.
- Write the kinetic energy formula
The formula for kinetic energy (KE) is:
$$ KE = 0.5 \times m \times v^2 $$
where $m$ is the mass of the car, and $v$ is its speed.
- Calculate the initial kinetic energy
Using the initial speed:
$$ KE_1 = 0.5 \times m \times (30)^2 $$
This simplifies to:
$$ KE_1 = 0.5 \times m \times 900 = 450m $$
- Calculate the final kinetic energy
Using the final speed:
$$ KE_2 = 0.5 \times m \times (60)^2 $$
This simplifies to:
$$ KE_2 = 0.5 \times m \times 3600 = 1800m $$
- Find the change in kinetic energy
The change in kinetic energy ($\Delta KE$) is calculated as:
$$ \Delta KE = KE_2 - KE_1 $$
Substituting the values we found:
$$ \Delta KE = 1800m - 450m = 1350m $$
The change in kinetic energy is $1350m$.
More Information
The kinetic energy of an object increases with the square of its speed. This means that when the speed doubles (from 30 m/s to 60 m/s), the final kinetic energy is not just twice the initial kinetic energy, but quite a bit more, reflecting the quadratic relationship.
Tips
- Forgetting to square the speed in the kinetic energy formula.
- Not correctly distinguishing between initial and final kinetic energy calculations.
AI-generated content may contain errors. Please verify critical information
