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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 39b
Capitolo 2, Problema 39b

A particle's velocity is described by the function vₓ = (t² - 7t + 10) m/s, where t is in s. What is the particle's acceleration at each of the turning points?

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To find the turning points of the particle's motion, we need to determine when the velocity is zero. Set the velocity function vₓ = t² - 7t + 10 equal to zero and solve for t. This gives the equation: t²−7t+10=0.
Solve the quadratic equation t²−7t+10=0 using factoring, the quadratic formula, or another method. The solutions for t will give the times at which the velocity is zero, i.e., the turning points.
Next, calculate the acceleration of the particle at each turning point. Acceleration is the time derivative of velocity. Differentiate the velocity function vₓ = t² - 7t + 10 with respect to time t to find the acceleration function: a=dvₓdt=2t−7.
Substitute the values of t (from the turning points) into the acceleration function a=2t−7 to calculate the acceleration at each turning point.
Interpret the results. The calculated accelerations at the turning points indicate the rate of change of velocity at those specific times. This helps describe the particle's motion at the turning points.

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Velocity

Velocity is a vector quantity that describes the rate of change of an object's position with respect to time. It includes both the speed of the object and the direction of its motion. In this context, the velocity function vₓ = (t² ─ 7t + 10) m/s indicates how the particle's speed changes over time, which is essential for determining its turning points.
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Turning Points

Turning points occur when a particle changes direction, which corresponds to the points where its velocity is zero. To find these points, we set the velocity function equal to zero and solve for time t. Identifying these points is crucial for analyzing the particle's motion and calculating its acceleration at those specific moments.
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Acceleration

Acceleration is the rate of change of velocity with respect to time and is a vector quantity. It can be derived from the velocity function by taking its derivative. In this case, calculating the acceleration at the turning points will provide insight into how the particle's speed is changing as it reverses direction, which is key to understanding its overall motion.
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Intro to Acceleration
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