Ch 02: Kinematics in One Dimension

Knight Calc - Physics for Scientists and Engineers 5th Edition

Knight Calc5th EditionPhysics for Scientists and EngineersISBN: 9780137344796Not the one you use?Change textbook

Knight Calc 5th Edition

Ch 02: Kinematics in One Dimension

Problem 49a

Chapter 2, Problem 49a

You're driving down the highway late one night at 20 m/s when a deer steps onto the road 35 m in front of you. Your reaction time before stepping on the brakes is 0.50 s, and the maximum deceleration of your car is 10 m/s². How much distance is between you and the deer when you come to a stop?

Verified step by step guidance

Determine the distance traveled during the reaction time. Use the formula for distance traveled at constant velocity:

d = v t

, where

v

is the velocity (20 m/s) and

t

is the reaction time (0.50 s).

Calculate the stopping distance after the brakes are applied. Use the kinematic equation:

d = \frac{v^{2}}{}

, where

v

is the initial velocity (20 m/s) and

a

is the deceleration (-10 m/s²).

Add the distance traveled during the reaction time to the stopping distance to find the total distance traveled before coming to a stop.

Compare the total distance traveled to the initial distance between you and the deer (35 m). Subtract the total distance traveled from 35 m to determine how much distance is left between you and the deer when you come to a stop.

Interpret the result: If the total distance traveled is less than 35 m, there will be a positive distance remaining between you and the deer. If the total distance traveled is greater than 35 m, you will not stop in time and will collide with the deer.

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Key Concepts

Here are the essential concepts you must grasp in order to answer the question correctly.

Kinematics

Kinematics is the branch of physics that describes the motion of objects without considering the forces that cause the motion. It involves concepts such as displacement, velocity, acceleration, and time. In this scenario, understanding kinematics is essential to calculate the distance traveled by the car during both the reaction time and the braking phase.

Acceleration and Deceleration

Acceleration refers to the rate of change of velocity of an object, while deceleration is a specific type of acceleration that indicates a decrease in speed. In this problem, the car's maximum deceleration of 10 m/s² is crucial for determining how quickly the car can stop after the brakes are applied. This concept helps in calculating the stopping distance once the driver reacts to the deer.

Reaction Time

Reaction time is the interval between the perception of a stimulus and the initiation of a response. In this case, the driver's reaction time of 0.50 seconds is significant because it affects the total distance traveled before the brakes are applied. Understanding this concept is vital for accurately calculating the total distance from the initial position to the stopping point.

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Textbook Question

A cheetah spots a Thomson's gazelle, its preferred prey, and leaps into action, quickly accelerating to its top speed of 30 m/s, the highest of any land animal. However, a cheetah can maintain this extreme speed for only 15 s before having to let up. The cheetah is 170 m from the gazelle as it reaches top speed, and the gazelle sees the cheetah at just this instant. With negligible reaction time, the gazelle heads directly away from the cheetah, accelerating at 4.6 m/s² for 5.0 s, then running at constant speed. Does the gazelle escape? If so, by what distance is the gazelle in front when the cheetah gives up?

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Textbook Question

You are driving to the grocery store at 20 m/s. You are 110 m from an intersection when the traffic light turns red. Assume that your reaction time is 0.50 s and that your car brakes with constant acceleration. What magnitude braking acceleration will bring you to a stop exactly at the intersection?

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Textbook Question

The takeoff speed for an Airbus A320 jetliner is 80 m/s. Velocity data measured during takeoff are as shown. Is the jetliner's acceleration constant during takeoff? Explain.

Textbook Question

Find an expression for the minimum stopping distance d_stop of a car traveling at speed v₀ if the driver's reaction time is T_react and the magnitude of the acceleration during maximum braking is a constant a_brake.

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Textbook Question

FIGURE P2.45 shows a set of kinematic graphs for a ball rolling on a track. All segments of the track are straight lines, but some may be tilted. Draw a picture of the track and also indicate the ball's initial condition.

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Textbook Question

A car starts from rest at a stop sign. It accelerates at 4.0 m/s² for 6.0 s, coasts for 2.0 s, and then slows down at a rate of 3.0 m/s² for the next stop sign. How far apart are the stop signs?

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