(a) Explanation Write the equation to find jerk from acceleration. J = d a x d t Here, J is the Jerk, d a x differential element of acceleration, and d t is the differential time element. Rewrite the above expression in terms of d a x . d a x = J d t Integrate the left hand side of above expression from a i x to a x and right hand side from t = 0 to t . ∫ a i x a x d a x = ∫ 0 t J d t Here, a i x is the initial acceleration. Result of above integration is shown below. a x − a i x = J ( t − 0 ) a x = J t + a x i Write the equation for acceleration from velocity. a x = d v x d t Here, d v x is the differential velocity element. Rewrite the above expression in terms of d v x . d v x = a x d t Integrate the left hand side of above expression from v i x to v x and right hand side from t = 0 to t . ∫ v i x v x d v x = ∫ 0 t a x d t Here, v i x is the initial velocity. Rewrite the above expression by substituting J t + a x i for a x . ∫ v i x v x d v x = ∫ 0 t ( J t + a x i ) d t Result of above integration is shown below. v x – v x i = a x i t + 1 2 J t 2 v x = v x i + a x i t + 1 2 J t 2 Write the equation for velocity from displacement (b) To determine Prove the relation a x 2 = a x i 2 + 2 J ( v x − v x i ) .

Physics for Scientists and Engineers with Modern Physics, Technology Update

9th Edition

ISBN: 9781305401969

Author: SERWAY, Raymond A.; Jewett, John W.

Publisher: Cengage Learning

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Chapter 2, Problem 57P

(a)

To determine

Derive the expressions for acceleration, velocity, and position.

(b)

To determine

Prove the relation ax2=axi2+2J(vx−vxi).

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Chapter 2, Problem 56P

Chapter 2, Problem 58P

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Physics for Scientists and Engineers with Modern Physics, Technology Update

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Ch. 2 - When applying the equations of kinematics for an...Ch. 2 - Prob. 5OQ Ch. 2 - Prob. 6OQ Ch. 2 - When the pilot reverses the propeller in a boat...Ch. 2 - Prob. 8OQ Ch. 2 - A skateboarder starts from rest and moves down a...Ch. 2 - Prob. 10OQ Ch. 2 - Prob. 11OQ Ch. 2 - A pebble is dropped from rest from the top of a...Ch. 2 - A student at the top of a building of height h...Ch. 2 - You drop a ball from a window located on an upper...Ch. 2 - A pebble is released from rest at a certain height...Ch. 2 - A ball is thrown straight up in the air. For which...Ch. 2 - Prob. 17OQ Ch. 2 - Each of the strobe photographs (a), (b), and (c)...Ch. 2 - If the average velocity of an object is zero in...Ch. 2 - Prob. 2CQ Ch. 2 - If a car is traveling eastward, can its...Ch. 2 - Prob. 4CQ Ch. 2 - Prob. 5CQ Ch. 2 - You throw a ball vertically upward so that it...Ch. 2 - (a) Can the equations of kinematics (Eqs....Ch. 2 - (a) Can the velocity of an object at an instant of...Ch. 2 - Two cars are moving in the same direction in...Ch. 2 - Position, Velocity, and Speed The position versus...Ch. 2 - The speed of a nerve impulse in the human body is...Ch. 2 - A person walks first at a constant speed of 5.00...Ch. 2 - A particle moves according to the equation x =...Ch. 2 - The position of a pinewood derby car was observed...Ch. 2 - Prob. 6P Ch. 2 - A positiontime graph for a particle moving along...Ch. 2 - An athlete leaves one end of a pool of length L at...Ch. 2 - Find the instantaneous velocity of the particle...Ch. 2 - Prob. 10P Ch. 2 - Prob. 11P Ch. 2 - A car travels along a straight line at a constant...Ch. 2 - A person takes a trip, driving with a constant...Ch. 2 - Prob. 14P Ch. 2 - Prob. 15P Ch. 2 - A child rolls a marble on a bent track that is 100...Ch. 2 - Figure P2.9 shows a graph of vx versus t for the...Ch. 2 - (a) Use the data in Problem 3 to construct a...Ch. 2 - A particle starts from rest and accelerates as...Ch. 2 - An object moves along the x axis according to the...Ch. 2 - Prob. 21P Ch. 2 - Draw motion diagrams for (a) an object moving to...Ch. 2 - Each of the strobe photographs (a), (b), and (c)...Ch. 2 - Prob. 24P Ch. 2 - An electron in a cathode-ray tube accelerates...Ch. 2 - Prob. 26P Ch. 2 - A parcel of air moving in a straight tube with a...Ch. 2 - A truck covers 40.0 m in 8.50 s while smoothly...Ch. 2 - An object moving with uniform acceleration has a...Ch. 2 - In Example 2.7, we investigated a jet landing on...Ch. 2 - Prob. 31P Ch. 2 - Solve Example 2.8 by a graphical method. On the...Ch. 2 - Prob. 33P Ch. 2 - Why is the following situation impossible?...Ch. 2 - Prob. 35P Ch. 2 - Prob. 36P Ch. 2 - Prob. 37P Ch. 2 - Prob. 38P Ch. 2 - A glider of length moves through a stationary...Ch. 2 - A glider of length 12.4 cm moves on an air track...Ch. 2 - Prob. 41P Ch. 2 - At t = 0, one toy car is set rolling on a straight...Ch. 2 - Prob. 43P Ch. 2 - Prob. 44P Ch. 2 - Prob. 45P Ch. 2 - An attacker at the base of a castle wall 3.65 m...Ch. 2 - Prob. 47P Ch. 2 - Prob. 48P Ch. 2 - Prob. 49P Ch. 2 - The height of a helicopter above the ground is...Ch. 2 - Prob. 51P Ch. 2 - Prob. 52P Ch. 2 - Prob. 53P Ch. 2 - At time t = 0, a student throws a set of keys...Ch. 2 - Prob. 55P Ch. 2 - Prob. 56P Ch. 2 - Prob. 57P Ch. 2 - A student drives a moped along a straight road as...Ch. 2 - The speed of a bullet as it travels down the...Ch. 2 - Prob. 60AP Ch. 2 - The froghopper Philaenus spumarius is supposedly...Ch. 2 - Prob. 62AP Ch. 2 - Prob. 63AP Ch. 2 - In Figure 2.11b, the area under the velocitytime...Ch. 2 - Prob. 65AP Ch. 2 - A woman is reported to have fallen 144 ft from the...Ch. 2 - An elevator moves downward in a tall building at a...Ch. 2 - Prob. 68AP Ch. 2 - Prob. 69AP Ch. 2 - Prob. 70AP Ch. 2 - At t = 0, one athlete in a race running on a long,...Ch. 2 - Prob. 72AP Ch. 2 - Prob. 73AP Ch. 2 - Prob. 74AP Ch. 2 - Two objects, A and B, are connected by hinges to a...Ch. 2 - Prob. 76AP Ch. 2 - Prob. 77AP Ch. 2 - Prob. 78AP Ch. 2 - Prob. 79AP Ch. 2 - Prob. 80AP Ch. 2 - Prob. 81CP Ch. 2 - Prob. 82CP Ch. 2 - In a womens 100-m race, accelerating uniformly,...Ch. 2 - Two thin rods are fastened to the inside of a...Ch. 2 - Prob. 85CP

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Derive the expressions for acceleration, velocity, and position.

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Derive the expressions for acceleration, velocity, and position.

Prove the relation ax2=axi2+2J(vx−vxi).

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Chapter 2 Solutions