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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 36b
Capitolo 2, Problema 36b

The position of a particle is given by the function x = (2t3 - 6t2 + 12) m, where t is in s. At what time is the acceleration zero?

Guida verificata passo dopo passo
1
Step 1: Start by recalling that acceleration is the second derivative of the position function with respect to time. The position function is given as x(t) = 2t^3 - 6t^2 + 12.
Step 2: Compute the first derivative of the position function to find the velocity function. Use the power rule for differentiation: v(t) = dx/dt = d/dt(2t^3 - 6t^2 + 12).
Step 3: Differentiate the velocity function to find the acceleration function. Again, use the power rule: a(t) = dv/dt = d/dt(6t^2 - 12t).
Step 4: Set the acceleration function equal to zero to find the time when the acceleration is zero. Solve the equation a(t) = 0 for t.
Step 5: Solve the resulting equation for t, ensuring you check for all possible solutions. These values of t represent the times when the acceleration is zero.

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Position Function

The position function describes the location of a particle as a function of time. In this case, the position x is given by the polynomial equation x = 2t^3 - 6t^2 + 12, which indicates how the particle's position changes over time. Understanding this function is crucial for determining the particle's velocity and acceleration.
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Intro to Wave Functions

Velocity

Velocity is the rate of change of position with respect to time, mathematically represented as the first derivative of the position function. For the given position function, the velocity v can be found by differentiating x with respect to t. This step is essential for analyzing the motion of the particle and determining when the acceleration is zero.
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Escape Velocity

Acceleration

Acceleration is the rate of change of velocity with respect to time, represented as the second derivative of the position function. To find when the acceleration is zero, one must differentiate the velocity function obtained from the position function and set it equal to zero. This indicates points in time where the particle is not changing its velocity, which is critical for understanding its motion.
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Intro to Acceleration
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