Solve the following problems on displacement, velocity, and acceleration. (1) The position of a particle which moves along a straight line is defined by the relation x=t³-6t²-15t + 40, where x is expressed in feet and t in seconds. Determine: (a) the time at which the velocity will be zero, (b) the position and distance traveled by the particle at that time, (c) the acceleration of the particle at that time, (d) the distance traveled by the particle from t = 4s to t = 6s. (2) The brake mechanism used to reduce recoil in certain types of guns consists essentially of a piston which is attached to the barrel and may move in a fixed cylinder filled with oil. As the barrel recoils with an initial velocity vo, the piston moves and oil is forced through orifices in the piston causing the piston and the barrel to decelerate at a rate proportional at a rate proportional to their velocity, that is, a = -kv. Express (a) v in terms of t, (b) x in terms of t. (c) v in terms of x. Draw the corresponding motion curves. Oil Piston

Solve the following problems on displacement, velocity, and acceleration. (1) The position of a particle which moves along a straight line is defined by the relation x=t³-6t²-15t + 40, where x is expressed in feet and t in seconds. Determine: (a) the time at which the velocity will be zero, (b) the position and distance traveled by the particle at that time, (c) the acceleration of the particle at that time, (d) the distance traveled by the particle from t = 4s to t = 6s. (2) The brake mechanism used to reduce recoil in certain types of guns consists essentially of a piston which is attached to the barrel and may move in a fixed cylinder filled with oil. As the barrel recoils with an initial velocity vo, the piston moves and oil is forced through orifices in the piston causing the piston and the barrel to decelerate at a rate proportional at a rate proportional to their velocity, that is, a = -kv. Express (a) v in terms of t, (b) x in terms of t. (c) v in terms of x. Draw the corresponding motion curves. Oil Piston

Elements Of Electromagnetics

7th Edition

ISBN:9780190698614

Author:Sadiku, Matthew N. O.

Publisher:Sadiku, Matthew N. O.

ChapterMA: Math Assessment

Section: Chapter Questions

Problem 1.1MA

See similar textbooks

Similar questions

The displacement of a particle is given by s=3t3-57t² + 114t 44 where s is in feet and it is in seconds. Plot the displacement, velocity. and acceleration as functions of time for the first 18 seconds of motion. After you have made the plots, answer the questions. Questions: Att 4.5 sec. Att 9 sec, Att 14.3 sec, A34 The velocity is zero when t 1 ft.v= ft. v ft, v= === sec and when t= !!! ft/sec, a= ft/sec. a ft/sec. a ft/sec ft/sec ft/sec
1. The position of a particle moving along the x-axis is described by x = t – 108t in where t is the time in sec. For the time interval t= 0 to t = 10 s, (a) plot the position, velocity, and acceleration as a function of time (b) find the displacement of the particle and (c) determine the distance traveled by the particle.
The position of a particle is given by s= 0.39³ -0.69t2-2.04t+4.42, where s is in feet and the time t is in seconds. Plot the displacement, velocity, and acceleration as functions of time for the first 6 seconds of motion. After you have the plots, answer the questions as a check on your work. Questions: 0 Whent 0.8 sec, v= When t 5.2 sec, v= 2 3 -+s, ft ft/sec. a ft/sec, a The positive time at which the particle changes direction is i sec. ft/sec2 ft/sec²
During a manufacturing process, a component moves in a linear pathsuch that its displacement “s” in mm is described as a function of time “t” inseconds by the equation: s = 3t3- t2 + 5t + 2 (mm) If a time of 1.5 seconds has elapsed in the process, determine :(i) the velocity of the component;(ii) the acceleration of the component.
The displacement of a particle is given by s = 2t³-42t² + 117t-49 where s is in feet and t is in seconds. Plot the displacement, velocity, and acceleration as functions of time for the first 18 seconds of motion. After you have made the plots, answer the questions. Questions: Att = 4.9 sec, S= Att = 9.4 sec, S= Att = 14.2 sec, S= i The velocity is zero when t = i fty = fty = i fty = i sec and when t = i ft/seca = ft/seca = ft/seca = i i sec ft/se ft/se ft/se
The displacement of a particle is given by s = 4t³-55t² + 115t-35 where s is in feet and t is in seconds. Plot the displacement, velocity, and acceleration as functions of time for the first 12 seconds of motion. After you have made the plots, answer the questions. Questions: Att 1.7 sec, Att = 5.4 sec, Att = 8.5 sec, S= S= S= i i The velocity is zero when t = i fty= M ftv i fty = i sec and when t = i ft/seca = ft/seca i ft/seca = i sec ft/sec ft/sec ft/sec
The displacement of a particle is given by s = 3t³ - 47t² +88t - 61 where s is in feet and t is in seconds. Plot the displacement, velocity, and acceleration as functions of time for the first 14 seconds of motion. After you have made the plots, answer the questions. Questions: At t = 3.3 sec, S = i At t = 7.2 sec, Att = 11.9 sec, S= i S= i The velocity is zero when t = i ft, v = ft, v = i i ft, v = i sec and when t = i ft/sec, a = ft/sec, a = i ft/sec, a = i sec ft/sec ft/sec ft/sec
The displacement of a particle is given by s = 5t3 - 70t2 + 105t - 57 where s is in feet and tis in seconds. Plot the displacement, velocity, and acceleration as functions of time for the first 11 seconds of motion. After you have made the plots, answer the questions. Questions: Att = 2.9 i ft, v = i ft/sec, a = i ft/sec sec, Att = 6.5 ft, v = ft/sec, a = ft/sec sec, Att=7.8 ft, v = i ft/sec,a = ft/sec sec, The velocity is zero when t= sec and when t = sec
The displacement of a particle is given by s = 3t3 - 50t2 + 91t - 53 where s is in feet and t is in seconds. Plot the displacement, velocity, and acceleration as functions of time for the first 13 seconds of motion. After you have made the plots, answer the questions. Questions: Att= 2.4 sec, i ftv = i ft/seca = i ft/sec Att= 6 sec, i ftv = i ft/seca = i ft/sec S= Att= 10.4 i ft.v = i ft/seca = i ft/sec sec, > The velocity is zero when t = i sec and when t = i sec eTextbook and Media Save for Later Attempts: 0 of 10 used Submit Answer
The position of a particle is given by s = 0.39t3 - 0.66t2 - 2.01t + 5.28, where s is in feet and the time t is in seconds. Plot the displacement, velocity, and acceleration as functions of time for the first 6 seconds of motion. After you have the plots, answer the questions as a check on your work. + s, ft -1 1 3 Questions: When t = 0.4 sec, V = i ft/sec, a = i ft/sec2 When t = 3.1 sec, V = i ft/sec, a = i ft/sec2 The positive time at which the particle changes direction is i sec.
The displacement of a particle is given by s = 4t3 - 54t2 + 105t - 49 where s is in feet and t is in seconds. Plot the displacement, velocity, and acceleration as functions of time for the first 10 seconds of motion. After you have made the plots, answer the questions. Questions: Att- 2 sec, ft. v= ft/sec, a = ft/sec? %3D Att = 4.1 i ft. v= i ft/sec, a = i ft/sec? sec, Att = 8.7 i ft, v= i ft/sec, a = i ft/sec? sec, The velocity is zero when t = i sec and whent%3D i sec
The velocity of a particle is given by v = 39t2-93t+ 47, where v is in meters per second and t is in seconds. Plot the velocity v and acceleration a versus time for the first 3 seconds of motion and evaluate the velocity when a is zero. Make the plots and then answer the questions. Questions: When t = 0.5 s, V = 10.25 m/s, a= -54 m/s² When t = 1.3 s, V= -7.99 m/s, a = 8.4 m/s² When t = 2.3 s, V= 39.41 m/s, a = 86.64 m/s² When a = 0, V= i 58.25 m/s