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2 - roofner(bar784 Homework 2 Weathers(17104 d(40.7 m/s...

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roofner (bar784) – Homework 2 – Weathers – (17104) 1 This print-out should have 10 questions. Multiple-choice questions may continue on the next column or page – find all choices before answering. 001 (part 1 of 2) 10.0 points The velocity of a particle moving along the x axis varies in time according to the expression v ( t ) = ( α - β t 2 ) where α = 40 . 7 m / s, β = 5 . 37 m / s 3 , and t is in seconds. Find the average acceleration in the time interval from t = 0 to 3 . 77 s. Correct answer: - 20 . 2449 m / s 2 . Explanation: The velocities at t i = 0 and t f = 3 . 77 s are found by substituting these values into the expression given for the velocity: v i = ( α - β t 2 i ) = (40 . 7 m / s - (5 . 37 m / s 3 ) (0 s) 2 ) = 40 . 7 m / s , v f = ( α - β t 2 f ) = (40 . 7 m / s - (5 . 37 m / s 3 ) (3 . 77 s) 2 ) = - 35 . 6233 m / s . Therefore, the average acceleration in the specified time interval Δ t = t f - t i = 3 . 77 s is ¯ a = v f - v i t f - t i = - 35 . 6233 m / s - 40 . 7 m / s 3 . 77 s - 0 s = - 20 . 2449 m / s 2 . 002 (part 2 of 2) 10.0 points Determine the acceleration of the particle at t f = 3 . 77 s. Correct answer: - 40 . 4898 m / s 2 . Explanation: We can use the rules of the differential calcu- lus to find the velocity from the displacement, at t = 3 . 77 s , the acceleration is a ( t ) = d v d t = d d t (40 . 7 m / s - 5 . 37 m / s 3 t 2 ) = - (2) (5 . 37 m / s 3 ) t = - (2) (5 . 37 m / s 3 ) (3 . 77 s) = - 40 . 4898 m / s 2 . 003 (part 1 of 2) 10.0 points An electron in the cathode ray tube of a tele- vision set enters a region where it acceler- ates uniformly from a speed of 42200 m / s to a speed of 3 . 42 × 10 6 m / s in a distance of 3 . 25 cm. What is its acceleration? Correct answer: 1 . 79917 × 10 14 m / s 2 . Explanation: Basic Concepts: Constant acceleration The kinematics equations v f = v o + at v 2 f = v 2 o + 2 as Solution: Taking the direction of motion to be along the x axis, the second equation yields a = v 2 f - v 2 o 2 x
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