Question

A car is traveling 20.0 m/s when the driver sees a child standing on the road.

A) In an attempt to stop, the car applies the brakes for 30 seconds
B) The car stops immediately to avoid any collision
C) The driver maintains the speed to avoid startling the child
D) The car decelerates at a rate of5 m/s²

Answer 1

Stopping distance in physics is the sum of the reaction distance and braking distance, which are calculated using the initial speed, the driver's reaction time, and the vehicle's deceleration rate. The rate of deceleration is affected by road conditions, with dry conditions allowing for greater deceleration than wet ones.

Step-by-step explanation:

Understanding a vehicle's stopping distance is critical for safety and is a common problem in physics related to motion and forces. Stopping distance is the total distance a vehicle travels from the moment a driver perceives a need to stop to the point where the vehicle comes to a complete halt.

The stopping distance can be divided into two parts: the reaction distance and the braking distance. The reaction distance is the distance traveled during the driver's reaction time, which is the time taken for the driver to move his foot to the brake after realizing the need to stop. For most drivers, a common reaction time used in calculations is 0.500 seconds. The braking distance is the distance the car travels after the brakes have been applied until it comes to a complete stop.

The stopping distance can be found using the following formulas:

1. Reaction Distance = Initial Speed × Reaction Time.
2. Braking Distance = (Initial Speed)^2 / (2 × Deceleration due to braking).
3. Total Stopping Distance = Reaction Distance + Braking Distance.

To calculate braking distance, you'll need to know the initial speed of the vehicle and the rate of deceleration. If the road conditions are dry, vehicles can typically decelerate at a higher rate compared to wet conditions due to less friction.

For example, if a car is moving at 30.0 m/s and can decelerate at 7.00 m/s² on dry concrete:

• The braking distance would be (30.0 m/s)^2 / (2 × 7.00 m/s²), or approximately 64.29 meters.
• Considering the reaction time of 0.500 seconds, the reaction distance would be 30.0 m/s × 0.500 s, or 15 meters.
• Therefore, the total stopping distance would be 64.29 meters + 15 meters, equaling roughly 79.29 meters.