EXAMPLE 5 Studying Particle MotionA particle moves along a line so that its position at any time tz 0 is given by the func-tion s(t) = r – 41 + 3, where s is measured in meters and t is measured in seconds.(a) Find the displacement of the particle during the first 2 seconds.(b) Find the average velocity of the particle during the first 4 seconds.(e) Find the instantaneous velocity of the particle when t = 4.(d) Find the acceleration of the particle when 1 = 4.(e) Describe the motion of the particle. At what values of t does the particle changedirections?(1) Use parametric graphing to view the motion of the particle on the horizontal line y = 2.

The displacement of the particle is st=t2-4t+3 Part a) Substituting the value of t = 2 in the above…

Answered: EXAMPLE 5 Studying Particle Motion A…

College Physics

1st Edition

ISBN:9781938168000

Author:Paul Peter Urone, Roger Hinrichs

Publisher:Paul Peter Urone, Roger Hinrichs

Chapter3: Two-dimensional Kinematics

Section: Chapter Questions

Problem 54PE: Near the end of a marathon race, the first two runners are separated by a distance of 45.0 m. The...

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Bryan Allen pedaled a human-powered aircraft across the English Channel from the cliffs of Dover to Cap Gris-Nez on June 12, 1979. (a) He flew for 169 min at an average velocity of 3.53 m/s in a direction 45° south of east. What was his total displacement? (b) Allen encountered a headwind averaging 2.00 m/s almost precisely in the opposite direction of his motion relative to the Earth. What was his average velocity relative to the air? (c) What was his total displacement relative to the air mass?
A dancer moves in one dimension back and forth across the stage. If the end of the stage nearest to her is considered to be the origin of an x axis that runs parallel to the stage, her position, as a function of time, is given by x(t)=[(0.02m/s3)t3(0.35m/s2)t2+(1.75m/s)t2.00m]i a. Find an expression for the dancers velocity as a function of time. b. Graph the velocity as a function of time for the 14 s over which the dancer performs (the dancer begins when t = 0) and use the graph to determine when the dancers velocity is equal to 0 m/s.
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Near the end of a marathon race, the first two runners are separated by a distance of 45.0 m. The front runner has a velocity of 3.50 m/s, and the second a velocity of 4.20 m/s. (a) What is the velocity of the second runner relative to the first? (b) If the front runner is 250 m from the finish line, who will win the race, assuming they run at constant velocity? (c) What distance ahead will the winner be when she crosses the finish line?
Chinook salmon are able to move through water especially fast by jumping out of the water periodically. This behavior is called porpoising. Suppose a salmon swimming in still water jumps out of the water with velocity 6.26 m/s at 45.0 above the horizontal, sails through the air a distance L before returning to the water, and then swims the same distance L underwater in a straight, horizontal line with velocity 3.58 m/s before jumping out again. (a) Determine the average velocity of the fish for the entire process of jumping and swimming underwater. (b) Consider the time interval required to travel the entire distance of 2L. By what percentage is this time interval reduced by the jumping/swimming process compared with simply swimming underwater at 3.58 m/s?
There is a distinction between average speed and the magnitude of average velocity. Give an example fiat illustrates the difference between these two quantities.
Please explain how to do this question. A particle moving in a straight line passes through a fixed point O The displacement s metres of the particle, t seconds after it passes through O, is given by s = 5t – 3 cos 2t + 3. (ii) Find the maximum velocity of the particle and the value of t at which this first occurs.
3.) A PARTICLE IS MOVING ALONG A HORIZONTAL LINE ACCORDING TO THE GIVEN EQUATION.The Equation is S = t^3 - 9t^2 + 15t ; t>=0.where (s) meters is the directed distance of the particle from the originat (t) seconds. where (v) meters per second is the instantaneous acceleration of the particle. 1. FIND (v) AND (a) IN TERMS OF (t).2. MAKE A TABLE THAT GIVES A Description of THE POSITION AND MOTION of the particle, include in the table the intervals of time when the PARTICLE IS MOVING TO THE LEFT AND RIGHT include in the table when the VELOCITY IS INCREASING AND DECREASING include in the table when the SPEED IS INCREASING AND DECREASING include in the table the POSITION OF THE PARTICLE with respect to the origin during these intervals of time. and Show the BEHAVIOR OF THE MOTION
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1. In a game of baseball, a player hits a high fly ball to the outfield.Is there a point during the flight of the ball where its velocityis parallel to its acceleration? Is there a point where the ball’svelocity is perpendicular to its acceleration? Explain in each case and graph it.
3.) This is differential Calculus subject. A PARTICLE IS MOVING ALONG A HORIZONTAL LINE ACCORDING TO THE GIVEN EQUATION.The Equation is S = t^3 - 9t^2 + 15t ; t>=0.where (s) meters is the directed distance of the particle from the originat (t) seconds. where (v) meters per second is the instantaneous acceleration of the particle. 1. FIND (v) AND (a) IN TERMS OF (t).2. MAKE A TABLE THAT GIVES A Description of THE POSITION AND MOTION of the particle, include in the table the intervals of time when the PARTICLE IS MOVING TO THE LEFT AND RIGHT include in the table when the VELOCITY IS INCREASING AND DECREASING include in the table when the SPEED IS INCREASING AND DECREASING include in the table the POSITION OF THE PARTICLE with respect to the origin during these intervals of time. and Show the BEHAVIOR OF THE MOTION

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