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Ch 02: Kinematics in One Dimension
Knight Calc - Physics for Scientists and Engineers 5th Edition
Knight Calc5th EditionPhysics for Scientists and EngineersISBN: 9780137344796Non è quello che usi tu?Cambia libro di testo
Tutti i libri di testoKnight Calc 5th EditionCh 02: Kinematics in One DimensionProblema 68b
Capitolo 2, Problema 68b

David is driving a steady 30 m/s when he passes Tina, who is sitting in her car at rest. Tina begins to accelerate at a steady 2.0 m/s² at the instant when David passes. What is her speed as she passes him?

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Step 1: Define the motion equations for both David and Tina. David is moving at a constant velocity, so his position as a function of time is given by: xd=30t. Tina starts from rest and accelerates uniformly, so her position as a function of time is: xt=12at2, where a=2.0 m/s².
Step 2: Set the positions of David and Tina equal to each other to find the time t when Tina passes David. This gives the equation: 30t=122.0t2.
Step 3: Simplify the equation to solve for t. Rearrange to get: t2=301t. Solve for t by factoring or using algebraic methods.
Step 4: Once you have the time t, calculate Tina's velocity at that moment using the formula for velocity under constant acceleration: v=u+at, where u=0 (initial velocity) and a=2.0 m/s².
Step 5: Substitute the value of t into the velocity equation to find Tina's speed as she passes David. This will give you the final answer.

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Relative Motion

Relative motion refers to the calculation of the motion of an object as observed from a particular reference point. In this scenario, David is moving at a constant speed while Tina is initially at rest. Understanding relative motion is crucial to determine how fast Tina needs to accelerate to catch up to David.
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Percorso guidato
04:27
Intro to Relative Motion (Relative Velocity)

Acceleration

Acceleration is the rate of change of velocity of an object with respect to time. In this case, Tina accelerates at a steady rate of 2.0 m/s². This concept is essential for calculating how her speed increases over time as she starts from rest.
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Percorso guidato
05:47
Intro to Acceleration

Kinematic Equations

Kinematic equations describe the motion of objects under constant acceleration. They relate displacement, initial velocity, final velocity, acceleration, and time. To find Tina's speed as she passes David, we can use these equations to determine her final velocity after a certain time of acceleration.
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Percorso guidato
08:25
Kinematics Equations
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