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Ch. 02 - Describing Motion: Kinematics in One Dimension
Giancoli Douglas - Physics for Scientists and Engineers 5th edition
Giancoli Douglas5th editionPhysics for Scientists and EngineersISBN: 9780137488179Not the one you use?Change textbook
All textbooksGiancoli Douglas 5th editionCh. 02 - Describing Motion: Kinematics in One DimensionProblem 41c
Chapter 2, Problem 41c

A car traveling 85 km/h slows down at a constant 0.50 m/s² just by 'letting up on the gas.' Calculate the distance it travels during the first and fifth seconds.

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1
Convert the car's initial velocity from km/h to m/s. Use the conversion factor: 1 km/h = 0.27778 m/s. The formula is: \( v_0 = 85 \times 0.27778 \).
Use the kinematic equation \( x = v_0 t + \frac{1}{2} a t^2 \) to calculate the distance traveled during the first second. Here, \( v_0 \) is the initial velocity, \( a \) is the acceleration (-0.50 m/s²), and \( t \) is the time (1 second).
To find the distance traveled during the fifth second, calculate the total distance traveled in 5 seconds using the same kinematic equation \( x = v_0 t + \frac{1}{2} a t^2 \). Then, calculate the total distance traveled in 4 seconds using the same equation. Subtract the distance traveled in 4 seconds from the distance traveled in 5 seconds to get the distance traveled during the fifth second.
Substitute the known values into the equations: \( v_0 \) (converted from step 1), \( a = -0.50 \ \text{m/s}^2 \), and \( t \) (1 second for the first second, and 5 seconds for the fifth second).
Simplify the expressions to find the distances for the first and fifth seconds. Remember to keep track of units and signs (negative acceleration indicates slowing down).

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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 mechanics that deals with 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, understanding kinematic equations is essential to calculate the distance traveled by the car during specific time intervals.
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Acceleration

Acceleration is defined as the rate of change of velocity of an object with respect to time. It can be positive (speeding up) or negative (slowing down), as in this case where the car decelerates at a constant rate of 0.50 m/s². This concept is crucial for determining how the car's speed changes over time and affects the distance traveled.
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Equations of Motion

The equations of motion describe the relationship between an object's displacement, initial velocity, acceleration, and time. For uniformly accelerated motion, the equation s = ut + 0.5at² can be used, where s is the distance, u is the initial velocity, a is the acceleration, and t is the time. These equations are vital for calculating the distance the car travels during the specified seconds.
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Related Practice
Textbook Question

A baseball pitcher throws a baseball with a speed of 43 m/s. Estimate the average acceleration of the ball during the throwing motion. In throwing the baseball, the pitcher accelerates it through a displacement of about 3.5 m, from behind the body to the point where it is released (Fig. 2–44).

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Textbook Question

For an object falling freely from rest, show that the distance traveled during each successive second increases in the ratio of successive odd integers (1, 3, 5, etc.). (This was first shown by Galileo.) See Figs. 2–27 and 2–30.

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Textbook Question

Figure 2–42 shows the velocity of a train as a function of time. During what periods, if any, was the velocity constant?

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Textbook Question

A rocket rises vertically, from rest, with an acceleration of 3.2 m/s² until it runs out of fuel at an altitude of 725 m. After this point, its acceleration is that of gravity, downward. What maximum altitude does the rocket reach?

Textbook Question

A helicopter is ascending vertically with a constant speed of 6.40 m/s. At a height of 105 m above the Earth, a package is dropped from the helicopter. How much time does it take for the package to reach the ground? [Hint: What is v₀ for the package?]

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Textbook Question

Figure 2–42 shows the velocity of a train as a function of time. During what periods, if any, was the acceleration constant?

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