(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

9th Edition

ISBN: 9781133953982

Author: SERWAY, Raymond A./

Publisher: Cengage Learning

See similar textbooks

Concept explainers

Projectile Motion

Videos

Question

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).

Expert Solution & Answer

Want to see the full answer?

Check out a sample textbook solution

See solution

Chapter 2, Problem 56P

Chapter 2, Problem 58P

Students have asked these similar questions

Identical rays of light enter three transparent blocks composed of different materials. Light slows down upon entering the blocks.

For single-slit diffraction, calculate the first three values of (the total phase difference between rays from each edge of the slit) that produce subsidiary maxima by a) using the phasor model, b) setting dr = 0, where I is given by, I = Io (sin (10) ². 2

A capacitor with a capacitance of C = 5.95×10−5 F is charged by connecting it to a 12.5 −V battery. The capacitor is then disconnected from the battery and connected across an inductor with an inductance of L = 1.55 H . (D)What is the charge on the capacitor 0.0235 s after the connection to the inductor is made? Interpret the sign of your answer. (e) At the time given in part (d), what is the current in the inductor? Interpret the sign of your answer. (f) Atthe time given in part (d), how much electrical energy is stored in the capacitor and how much is stored in the inductor?

Chapter 2 Solutions

Physics for Scientists and Engineers With Modern Physics

Ch. 2.1 - Under which of the following conditions is the...Ch. 2.2 - Are officers in the highway patrol more interested...Ch. 2.4 - Make a velocitytime graph for the car in Figure...Ch. 2.4 - If a car is traveling eastward and slowing down,...Ch. 2.5 - Which one of the following statements is true? (a)...Ch. 2.6 - In Figure 2.12, match each vxt graph on the top...Ch. 2.7 - Consider the following choices: (a) increases, (b)...Ch. 2 - Prob. 1OQ Ch. 2 - A racing car starts from rest at t = 0 and reaches...Ch. 2 - Prob. 3OQ

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

Knowledge Booster

Learn more about

Need a deep-dive on the concept behind this application? Look no further. Learn more about this topic, physics and related others by exploring similar questions and additional content below.

Derive the expressions for acceleration, velocity, and position.

Solution Summary: The author explains how to derive the expressions for acceleration, velocity, and position.

Concept explainers

Videos

Derive the expressions for acceleration, velocity, and position.

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

Want to see the full answer?

Chapter 2 Solutions