A shopping cart moves with a kinetic energy of 40 J. If it moves at twice the speed, its kinetic energy is?
Understand the Problem
The question is asking about the change in kinetic energy of a shopping cart when its speed is doubled. It provides the initial kinetic energy and multiple-choice answers to determine the new kinetic energy.
Answer
When the shopping cart's speed is doubled, its kinetic energy becomes $160 \, J$.
Answer for screen readers
The new kinetic energy when the speed is doubled is $160 , J$.
Steps to Solve
-
Understand the Kinetic Energy Formula
Kinetic energy (KE) is given by the formula:
$$ KE = \frac{1}{2} mv^2 $$
where $m$ is mass and $v$ is velocity. -
Identify Initial Kinetic Energy
The problem states that the initial kinetic energy of the shopping cart is $40 , J$. -
Determine the Effect of Doubling Speed
If the speed is doubled, the new speed becomes $2v$. Plug this into the kinetic energy formula:
$$ KE_{new} = \frac{1}{2} m (2v)^2 $$
This simplifies to:
$$ KE_{new} = \frac{1}{2} m (4v^2) = 2mv^2 $$
which means:
$$ KE_{new} = 4 \left(\frac{1}{2} mv^2 \right) = 4 \times KE_{initial} $$ -
Calculate New Kinetic Energy
Now substitute the initial kinetic energy:
$$ KE_{new} = 4 \times 40 , J = 160 , J $$
The new kinetic energy when the speed is doubled is $160 , J$.
More Information
Doubling the speed results in a quadrupling of kinetic energy, which is an important concept in physics. This principle helps understand how energy changes with speed in various systems.
Tips
- Forgetting that kinetic energy is proportional to the square of the velocity. This often leads to underestimating or overestimating the changes in energy when speed changes.
- Assuming linear relationships where square relationships exist.
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