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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: 9780137344796Not the one you use?Change textbook
All textbooksKnight Calc 5th EditionCh 02: Kinematics in One DimensionProblem 35b
Chapter 2, Problem 35b

The vertical position of a particle is given by the function y = (t2 - 4t + 2) m, where t is in s. What is the particle's position at that time?

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1
Identify the given function for the vertical position of the particle: y(t) = t^2 - 4t + 2, where y is in meters and t is in seconds.
To find the particle's position at a specific time, substitute the given value of t into the function y(t). For example, if t = t₀, calculate y(t₀) = (t₀)^2 - 4(t₀) + 2.
Simplify the expression by performing the operations: square the value of t₀, multiply 4 by t₀, and then add or subtract the terms as indicated.
Ensure the units are consistent. Since the function is in meters and seconds, the result will be in meters.
Verify the calculation by rechecking the substitution and simplification steps to ensure accuracy.

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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 describes the motion of objects without considering the forces that cause the motion. It involves concepts such as displacement, velocity, and acceleration, which are essential for analyzing the position of a particle over time. In this context, the function y = (t^2 - 4t + 2) m represents the vertical position of the particle as a function of time.
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Quadratic Functions

A quadratic function is a polynomial function of degree two, typically expressed in the form f(t) = at^2 + bt + c. The graph of a quadratic function is a parabola, which can open upwards or downwards depending on the sign of the coefficient 'a'. In the given equation, the quadratic nature indicates that the particle's vertical position changes in a non-linear manner over time.
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Evaluating Functions

Evaluating a function involves substituting a specific value into the function to determine its output. In this case, to find the particle's position at a given time 't', one must substitute the value of 't' into the function y = (t^2 - 4t + 2) m. This process is fundamental in mathematics and physics for determining specific outcomes based on defined relationships.
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Related Practice
Textbook Question

A particle moving along the x-axis has its position described by the function x = (2t3 + 2t + 1) m, where t is in s. At t = 2s, what are the particle's position?

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Textbook Question

A block is suspended from a spring, pulled down, and released. The block's position-versus-time graph is shown in FIGURE P2.38. At what times is the velocity zero? At what times is the velocity most positive? Most negative?

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Textbook Question

The position of a particle is given by the function x = (2t3 = 6t2 + 12) m, where t is in s. At what time does the particle reach its minimum velocity? What is (vx)min?

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Textbook Question

FIGURE EX2.32 shows the acceleration graph for a particle that starts from rest at t = 0 s. What is the particle's velocity at t = 6 s?

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Textbook Question

A particle moving along the x-axis has its veocity described by the function vx = 2t2 m/s, where t is in s. itsinitial position is x0 = 1 m at t0 = 0 s. At t = 1 s, what are the particle's position?

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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?

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