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 51

Chapter 2, Problem 51

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?

Verified step by step guidance

Determine the distance traveled during the acceleration phase using the kinematic equation:

d = \frac{1}{2} a t^{2}

, where

a

is the acceleration (4.0 m/s²) and

t

is the time (6.0 s).

Calculate the velocity at the end of the acceleration phase using the equation:

v = u + a t

, where

u

is the initial velocity (0 m/s),

a

is the acceleration (4.0 m/s²), and

t

is the time (6.0 s).

Determine the distance traveled during the coasting phase using the equation:

d = v t

, where

v

is the velocity at the end of the acceleration phase (calculated in step 2) and

t

is the coasting time (2.0 s).

Calculate the distance traveled during the deceleration phase using the kinematic equation:

d = \frac{1}{2} (v + u) t

, where

v

is the final velocity (0 m/s),

u

is the velocity at the start of deceleration (calculated in step 2), and

t

is the time taken to decelerate (calculated using

t = \frac{u}{a}

, where

a

is the deceleration rate of 3.0 m/s²).

Add the distances from all three phases (acceleration, coasting, and deceleration) to find the total distance between the stop signs.

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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 problem, kinematic equations will be used to calculate the distance traveled by the car during different phases of its motion.

Acceleration

Acceleration is the rate of change of velocity of an object with respect to time. It can be positive (speeding up) or negative (slowing down). In this scenario, the car experiences different accelerations: a positive acceleration of 4.0 m/s² while speeding up, a period of zero acceleration while coasting, and a negative acceleration of 3.0 m/s² while slowing down.

Displacement

Displacement is a vector quantity that refers to the change in position of an object. It is calculated as the total distance traveled in a specific direction. In this question, the total displacement will be determined by calculating the distance covered during each phase of the car's motion and summing them to find the total distance between the stop signs.

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Displacement vs. Distance

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