A car, of mass m, traveling at a speed v1 can brake to a...

A car, of mass $m,$ traveling at a speed $v_{1}$ can brake to a stop within a distance $d$. If the car speeds up by a factor of $2, v_{2}=2 v_{1},$ by what factor is its stopping distance increased, assuming that the braking force $F$ is approximately independent of the car's speed?

Labs

Want to see this concept in action?

NEW

Explore this concept interactively to see how it behaves as you change inputs.

View Labs

Key Concepts

Kinetic Energy

Kinetic energy is the energy an object possesses due to its motion, typically expressed as (1/2)mv². This concept is essential because it quantifies the energy that needs to be dissipated by braking, and any increase in speed results in a significant increase in kinetic energy.

Work-Energy Principle

The work-energy principle states that the work done by all forces acting on an object equals the change in its kinetic energy. In braking, the constant force exerted by the brakes does work on the car, reducing its kinetic energy to zero, thereby linking stopping distance to the car's initial speed.

Relationship Between Speed and Stopping Distance

Because kinetic energy increases with the square of the speed, the stopping distance for a car (assuming a constant braking force) also increases with the square of the speed. This means that when the speed is doubled, the stopping distance becomes four times greater, illustrating the non-linear effect of speed on stopping distances.

Transcript

Please give Ace some feedback