Question

1. braking distance is the distance a car travels from the time a person applies the brakes to when the car comes to a complete stop. the graph shows the relationship between the speed of a car and the distance the car travels before it stops.

distance to stop

bar graph with speed (km/h) on x - axis: 33, 67, 83, 100, 116; distance traveled (m) on y - axis: 0 - 100. bars increase with speed.

based on the graph, describe the relationship between the car’s braking distance and kinetic energy. be sure to use evidence from the graph to support your response.

Explanation:

Kinetic energy ($KE$) is given by the formula $KE = \frac{1}{2}mv^2$, where $m$ is mass and $v$ is speed. Assuming the car's mass is constant, kinetic energy is proportional to the square of the speed. The bar graph shows that as speed (x - axis) increases (from 33 km/h to 116 km/h), the braking distance (y - axis, distance traveled to stop) also increases. Since kinetic energy increases with the square of speed, and braking distance increases with speed, we can infer that braking distance is related to kinetic energy such that as kinetic energy increases (due to increasing speed), the braking distance also increases. For example, at 33 km/h (lower speed, lower KE), the braking distance is small, and at 116 km/h (higher speed, higher KE), the braking distance is much larger. This is because more kinetic energy means more work (done by friction during braking) is needed to stop the car, and work is force times distance ($W = Fd$). If the braking force (friction) is approximately constant, a larger distance is required to do more work to dissipate higher kinetic energy.

Answer:

As the car's speed (and thus kinetic energy, since \( KE=\frac{1}{2}mv^2 \) and mass \( m \) is constant) increases, the braking distance also increases. Evidence from the graph: when speed is 33 km/h, braking distance is small; when speed is 116 km/h, braking distance is much larger. Higher kinetic energy requires more work (from friction) to stop the car, so a greater distance is needed (as \( W = Fd \), with braking force \( F \) roughly constant, more \( d \) is needed for more \( KE \) - related work).