If A Particle's Speed Increases By A Factor Of 4, By What Factor Does Its Kinetic Energy Change?

Kinetic Energy

Kinetic energy is the energy of motion. An object that has motion - whether it is vertical or horizontal motion - has kinetic energy. There are many forms of kinetic energy - vibrational (the energy due to vibrational move), rotational (the free energy due to rotational motility), and translational (the energy due to motion from ane location to another). To go on matters simple, we will focus upon translational kinetic energy. The amount of translational kinetic energy (from here on, the phrase kinetic energy volition refer to translational kinetic energy) that an object has depends upon two variables: the mass (k) of the object and the speed (v) of the object. The following equation is used to represent the kinetic energy (KE) of an object.

KE = 0.v • grand • v²

where m = mass of object

v = speed of object

This equation reveals that the kinetic energy of an object is direct proportional to the square of its speed. That means that for a twofold increment in speed, the kinetic energy volition increase by a factor of four. For a threefold increase in speed, the kinetic energy volition increase by a gene of nine. And for a fourfold increase in speed, the kinetic energy will increase by a factor of xvi. The kinetic energy is dependent upon the square of the speed. As it is often said, an equation is not simply a recipe for algebraic problem solving, but also a guide to thinking nearly the relationship between quantities.

Kinetic free energy is a scalar quantity; it does non take a management. Dissimilar velocity, acceleration, strength, and momentum, the kinetic energy of an object is completely described by magnitude alone. Similar work and potential energy, the standard metric unit for kinetic energy is the Joule. As might be unsaid past the higher up equation, ane Joule is equivalent to one kg*(m/s)^2.

1 Joule = 1 kg • m²/s²

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How does a motorcar'southward speed (and thus its kinetic energy) touch on the distance that would exist required for it to brake to a stop? Interact, Explore, and Learn the answer to this question with our Stopping Distance Interactive. You tin find it in the Physics Interactives section of our website. The Stopping Altitude Interactive allows a learner to explore the effect of speed upon the stopping distance of a toy machine.

Check Your Understanding

Utilize your understanding of kinetic energy to reply the following questions. So click the button to view the answers.

1. Determine the kinetic energy of a 625-kg roller coaster car that is moving with a speed of xviii.3 m/southward.

2. If the roller coaster motorcar in the higher up problem were moving with twice the speed, then what would be its new kinetic energy?

iii. Missy Diwater, the former platform diver for the Ringling Brother'southward Circus, had a kinetic energy of 12 000 J just prior to hitting the bucket of water. If Missy'due south mass is 40 kg, then what is her speed?

four. A 900-kg compact car moving at 60 mi/hr has approximately 320 000 Joules of kinetic energy. Estimate its new kinetic free energy if it is moving at 30 mi/60 minutes. (HINT: use the kinetic energy equation every bit a "guide to thinking.")