Textbook Question
FIGURE EX1.8 shows the first three points of a motion diagram. Is the object's average speed between points 1 and 2 greater than, less than, or equal to its average speed between points 0 and 1? Explain how you can tell.
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Ch 01: Concepts of Motion
Chapter 1, Problem 1
For Problems 34, 35, 36, 37, 38, 39, 40, 41, 42, and 43, draw a complete pictorial representation. Do not solve these problems or do any mathematics. A jet plane is cruising at 300 m/s when suddenly the pilot turns the engines up to full throttle. After traveling 4.0 km, the jet is moving with a speed of 400 m/s. What is the jet's acceleration as it speeds up?
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Identify the initial velocity of the jet plane, which is given as 300 m/s.
Determine the final velocity of the jet after the acceleration, which is stated to be 400 m/s.
Note the distance traveled during the acceleration, which is provided as 4.0 km. Convert this distance into meters for consistency in units.
Use the kinematic equation that relates initial velocity, final velocity, acceleration, and distance traveled: \( v_f^2 = v_i^2 + 2a \Delta x \), where \( v_f \) is the final velocity, \( v_i \) is the initial velocity, \( a \) is the acceleration, and \( \Delta x \) is the distance traveled.
Rearrange the equation to solve for the acceleration \( a \).
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Key Concepts
Here are the essential concepts you must grasp in order to answer the question correctly.
Acceleration
Acceleration is defined as the rate of change of velocity of an object with respect to time. It is a vector quantity, meaning it has both magnitude and direction. In the context of the jet plane, acceleration can be calculated by determining how much the speed of the jet increases over a specific distance or time interval.
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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, and acceleration. Understanding kinematics is essential for analyzing the motion of the jet plane as it speeds up from 300 m/s to 400 m/s over a distance of 4.0 km.
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Velocity
Velocity is a vector quantity that describes the speed of an object in a specific direction. It is different from speed, which is a scalar quantity and only considers magnitude. In this scenario, the initial and final velocities of the jet plane are crucial for determining the acceleration as it transitions from 300 m/s to 400 m/s.
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Related Practice
Textbook Question
FIGURE EX1.9 shows five points of a motion diagram. Use Tactics Box 1.2 to find the average acceleration vectors at points 1, 2, and 3. Draw the completed motion diagram showing velocity vectors and acceleration vectors.
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Textbook Question
FIGURE EX1.10 shows two dots of a motion diagram and vector . Copy this figure, then add dot 4 and the next velocity vector if the acceleration vector at dot 3 (b) points left.
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Textbook Question
You are watching a jet ski race. A racer speeds up from rest to 70 mph in 10 s, then continues at a constant speed. Draw a basic motion diagram of the jet ski, using s from the video, from its start until 10 s after reaching top speed.
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Textbook Question
A jet plane lands on the deck of an aircraft carrier and quickly comes to a halt. Draw a basic motion diagram, using the s from the video, from the time the jet touches down until it stops.
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Textbook Question
You drop a soccer ball from your third-story balcony. Use the particle model to draw a motion diagram showing the ball's position and average velocity vectors from the time you release the ball until the instant it touches the ground.
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