A car is travelling at 40.0 m s^-1. The driver sees an emergency ahead and 0.50 s later slams on

step 1 For this problem, we have a car that is traveling at 40 meters per second, and it notices someth

A car is travelling at 40.0 m s^-1. The driver sees an...

A car is travelling at $40.0 \mathrm{m} \mathrm{s}^{-1}$. The driver sees an emergency ahead and 0.50 s later slams on the brakes. The acceleration of the car is $-4 m s^{-2}.$ (a) What distance will the car travel before it stops? (b) If the driver was able to apply the brakes instantaneously without a reaction time, over what distance would the car stop? (c) Calculate the difference in your answers to (a) and (b). (d) Assume now that the car was travelling at $30.0 \mathrm{m} \mathrm{s}^{-1}$ instead. Without performing any calculations, would the answer to (c) now be less than, equal to or larger than before? Explain your answer.

A car is travelling at $40.0 \mathrm{m} \mathrm{s}^{-1}$. The driver sees an emergency ahead and 0.50 s later slams on the brakes. The acceleration of the car is $-4 m s^{-2}.$
(a) What distance will the car travel before it
stops?
(b) If the driver was able to apply the brakes instantaneously without a reaction time, over what distance would the car stop?
(c) Calculate the difference in your answers to
(a) and (b).
(d) Assume now that the car was travelling at $30.0 \mathrm{m} \mathrm{s}^{-1}$ instead. Without performing any calculations, would the answer to (c) now be less than, equal to or larger than before? Explain your answer.

Key Concepts

Constant Acceleration Kinematics

This concept encompasses the set of equations and principles used to describe motion under constant acceleration. It allows us to relate initial velocity, final velocity, acceleration, time, and displacement. These equations form the backbone of analyzing situations like braking, where deceleration is constant, and enable the computation of distances traveled during acceleration or deceleration phases.

Deceleration (Negative Acceleration)

Deceleration refers to a reduction in speed, typically represented by a negative acceleration value in the equations of motion. In scenarios involving braking, deceleration is used to determine how quickly an object, such as a vehicle, slows down, and it directly influences the computed stopping distance.

Reaction Time and Reaction Distance

Reaction time is the delay between when a driver perceives a threat and when they actually begin to take action, such as applying the brakes. During this period, the vehicle continues to travel at its original speed, covering a certain distance known as the reaction distance. This concept is critical in safety analyses as it contributes to the total stopping distance in real-world scenarios.

Stopping Distance

Stopping distance is the total distance a vehicle travels from the moment a driver perceives a hazard to the time the vehicle comes to a complete stop. It is composed of both the distance covered during the reaction time and the braking distance incurred once the brakes are applied. This measure is essential in designing safe following distances and speed limits, and it is sensitive to initial speed and deceleration factors.

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