Explanation Write the equation for final velocity. v x = v 0 x + a x t (I) Here, v x is the final velocity in x direction, v 0 x is the initial velocity is x direction, a x is the constant acceleration in the x direction and t is the time taken. Write the equation for velocity. v x = d x d t (II) Here, d x d t is the rate of change of displacement. Conclusion: Compare equation (I) and equation (II). d x d t = v 0 x + a x t d x = v 0 x d t + a x t d t Integrate on both sides to find the displacement

Physics for Scientists and Engineers: Foundations and Connections

15th Edition

ISBN: 9781305289963

Author: Debora M. Katz

Publisher: Cengage Custom Learning

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Chapter 2 Solutions

Physics for Scientists and Engineers: Foundations and Connections

Ch. 2.2 - In each of the five motion diagrams shown in...Ch. 2.3 - For each of the following, give the vector...Ch. 2.5 - Figure 2.11 shows the motion of various objects:...Ch. 2.6 - The top marathon runners complete the race in...Ch. 2.6 - In our everyday experience, we sometimes use the...Ch. 2.6 - Prob. 2.6CE Ch. 2.8 - Kinematics graphs are great for showing how a...Ch. 2 - Is the Moons motion around the Earth...Ch. 2 - An animals tracks are frozen in the snow (Fig....Ch. 2 - Problems 3 and 12 are paired. G A particle moves...

Ch. 2 - Prob. 4PQ Ch. 2 - For each of the following velocity vectors, give...Ch. 2 - In the traditional Hansel and Gretel fable, the...Ch. 2 - After a long and grueling race, two cadets, A and...Ch. 2 - Prob. 8PQ Ch. 2 - Elisha Graves Otis invented the elevator brake in...Ch. 2 - As shown in Figure 2.9, Whipple chose a coordinate...Ch. 2 - Prob. 11PQ Ch. 2 - Prob. 12PQ Ch. 2 - A race car travels 825 km around a circular sprint...Ch. 2 - Prob. 14PQ Ch. 2 - A train leaving Albuquerque travels 293 miles, due...Ch. 2 - Prob. 16PQ Ch. 2 - The position of a particle attached to a vertical...Ch. 2 - Prob. 18PQ Ch. 2 - Prob. 19PQ Ch. 2 - Prob. 20PQ Ch. 2 - During a relay race, you run the first leg of the...Ch. 2 - Prob. 22PQ Ch. 2 - Prob. 23PQ Ch. 2 - Prob. 24PQ Ch. 2 - During a thunderstorm, a frightened child is...Ch. 2 - Scientists and engineers must interpret problems...Ch. 2 - Prob. 27PQ Ch. 2 - Prob. 28PQ Ch. 2 - A In attempting to break one of his many swimming...Ch. 2 - A The instantaneous speed of a particle moving...Ch. 2 - A particles velocity is given by vy(t)=atj, where...Ch. 2 - Prob. 32PQ Ch. 2 - Figure P2.33 shows the y-position (in blue) of a...Ch. 2 - A particles position is given by z(t) = (7.50...Ch. 2 - Prob. 35PQ Ch. 2 - Two sprinters start a race along a straight track...Ch. 2 - An electronic line judge camera captures the...Ch. 2 - During a bungee jump, a student (i) initially...Ch. 2 - Prob. 39PQ Ch. 2 - Prob. 40PQ Ch. 2 - Prob. 41PQ Ch. 2 - Prob. 42PQ Ch. 2 - Prob. 43PQ Ch. 2 - Prob. 44PQ Ch. 2 - A computer system, using a preset coordinate...Ch. 2 - In Example 2.6, we considered a simple model for a...Ch. 2 - A uniformly accelerating rocket is found to have a...Ch. 2 - Prob. 48PQ Ch. 2 - A driver uniformly accelerates his car such that...Ch. 2 - Car A and car B travel in the same direction along...Ch. 2 - Accelerating uniformly to overtake a slow-moving...Ch. 2 - An object that moves in one dimension has the...Ch. 2 - A particle moves along the positive x axis with a...Ch. 2 - Case Study Crall and Whipple attached a fan to a...Ch. 2 - Prob. 55PQ Ch. 2 - The engineer of an intercity train observes a rock...Ch. 2 - A pebble is thrown downward from a 44.0-m-high...Ch. 2 - In a cartoon program, Peter tosses his baby,...Ch. 2 - Tadeh launches a model rocket straight up from his...Ch. 2 - Prob. 60PQ Ch. 2 - In the movie Star Wars: The Empire Strikes Back,...Ch. 2 - A worker tosses bricks one by one to a coworker on...Ch. 2 - A rock is thrown straight up into the air with an...Ch. 2 - Prob. 64PQ Ch. 2 - A sounding rocket, launched vertically upward with...Ch. 2 - Prob. 66PQ Ch. 2 - While strolling downtown on a Saturday Afternoon,...Ch. 2 - Prob. 68PQ Ch. 2 - A trooper is moving due south along the freeway at...Ch. 2 - A dancer moves in one dimension back and forth...Ch. 2 - The electrical impulse initiated by the nerves in...Ch. 2 - Two cars leave Seattle at the same time en route...Ch. 2 - An object begins to move along the y axis and its...Ch. 2 - Prob. 74PQ Ch. 2 - Prob. 75PQ Ch. 2 - Two carts are set in motion at t = 0 on a...Ch. 2 - Prob. 77PQ Ch. 2 - Cars A and B each move to the right with constant...Ch. 2 - Prob. 79PQ Ch. 2 - Prob. 80PQ Ch. 2 - Prob. 82PQ Ch. 2 - Prob. 83PQ Ch. 2 - A Write expressions for the average acceleration...Ch. 2 - Prob. 85PQ Ch. 2 - Prob. 86PQ Ch. 2 - In 1898, the world land speed record was set by...Ch. 2 - In Example 2.12, two circus performers rehearse a...Ch. 2 - Prob. 89PQ

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Show that Δ x = v 0 x t + 1 2 a x t 2 using integral calculus.

Solution Summary: The author compares the equations for velocity and displacement using integral calculus.

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Show that Δx=v0xt+12axt2 using integral calculus.

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Chapter 2 Solutions