Concept explainers
The motion of a vibrating particle is defined by the position
(a)
The velocity and acceleration when t=0.
Answer to Problem 11.90P
Explanation of Solution
Given information:
The motion of a vibrating particle is defined by the position vector,
Where, (r) in millimetres and (t) is in seconds.
We can obtain the velocity (v) at any time (t) by differentiating (r) with respect to (t),
Since,
The acceleration (a) can be obtained by differentiating again the above equation with respect to (t),
When t=0,
Velocity,
And, acceleration,
(b)
The velocity and acceleration when t=0.5.
Answer to Problem 11.90P
Explanation of Solution
Given information:
The motion of a vibrating particle is defined by the position vector,
Where, (r) in millimetres and (t) is in seconds.
We can obtain the velocity (v) at any time (t) by differentiating (r) with respect to (t),
Since,
The acceleration (a) can be obtained by differentiating again the above equation with respect to (t),
When t=0.5,
Velocity,
And, acceleration,
Want to see more full solutions like this?
Chapter 11 Solutions
Vector Mechanics For Engineers
- The position of a particle in rectilinear motion is defined by the relation x=((t^4)/12)− ((2t^3)/3)− ((5t^2)/2) + 3t +4 where x is in meters and t is in seconds. Determine its position and velocity when the acceleration is zero.arrow_forwardA car is moving along a straight line with a velocity v= 3t^2–t+ 5m/s, where t is in seconds.Determine the acceleration, velocity and the position of the particle when t = 6 s. When t = 0, v = 0, and s = 8m.arrow_forwardThe motion of a particle is defined by the relationship x= 5/3 t ^3 - 5/2 t ^2-30t + 8, where x and t are expressed in meters and seconds, respectively. Determine the time, position, and acceleration when v = 0.arrow_forward
- The damped motion of a vibrating particle is defined by the position vector r =x1[1 - 1/(t+ 1)]i+ (y1e-πt/2 cos 2π)j where t is expressed in seconds. For x1 = 30 mm and y1 = 20 mm, determine the position, the velocity, and the acceleration of the particle when (a) t= 0, (b) t=t 1.5 s.arrow_forwardThe vertical motion of mass A is defined by the relation x =10 sin 2t +15cos 2t +100, where x and t are expressed in mm and seconds, respectively. Determine (a) the position, velocity and acceleration of A when t = 1 s, (b) the maximum velocity and acceleration of A.arrow_forwardExperimental data indicate that in a region downstream of a given louvered supply vent the velocity of the emitted air is defined by v = 0.18 v0/x, where v and x are expressed in m/s and meters, respectively, and v0 is the initial discharge velocity of the air. For v0 = 3.6 m/s, determine (a) the acceleration of the air at x= 2 m, (b) the time required for the air to flow from x= 1 to x= 3 m.arrow_forward
- A projectile enters a resisting medium at x = 0 with an initial velocity v0 = 900 ft/s and travels 4 in. before coming to rest. Assuming that the velocity of the projectile is defined by the relation v=v0 - kx, where v is expressed in ft/s and x is in feet, determine (a) the initial acceleration of the projectile, (b) the time required for the projectile to penetrate 3.9 in. into the resisting medium.arrow_forwardThe velocity of a particle, measured from a rectangular coordinate system (X, Y, Z)is given by ? = [t3i + 8t2j + (5t + 2) k ]m/s, where t is given in seconds. If the particle is at the origin (x = 0, y = 0, z = 0) when t = 0 s, determine: (a) The intensity of the particle velocity when t = 4 s (b) The intensity of the particle acceleration when t = 4 s (c) The position of the particle in coordinates (x, y, z) when t = 4 sarrow_forwardA particle travels to the right along a straight line with a velocity v = [5/(4+s)]m/s where s is in meters. Determine its position when t = 6 s if s = 5 m when t = 0.arrow_forward
- The velocity of a particle which moves along the s axis is given by v = 4.1 -2.7t + 3.4t3/2, where t is in seconds and v is in meters per second. The particle is at the position s0 = 9 m when t = 0. Evaluate the position, s when t = 7.4 s.arrow_forwardUsing the formula a = kt where k is a constant, determine the velocity in m/s at 1 second knowing that at t=3s,v=18m/s, and the particle stops at t= 7 seconds.arrow_forwardBased on experimental observations, the acceleration of a particle is defined by the relation a = –(0.1 + sin x/b), where a and x are expressed in m/s2 and meters, respectively. Know that b = 0.80 m and that v = 1 m/s when x = 0. Determine the position where the velocity is maximum.arrow_forward
- Elements Of ElectromagneticsMechanical EngineeringISBN:9780190698614Author:Sadiku, Matthew N. O.Publisher:Oxford University PressMechanics of Materials (10th Edition)Mechanical EngineeringISBN:9780134319650Author:Russell C. HibbelerPublisher:PEARSONThermodynamics: An Engineering ApproachMechanical EngineeringISBN:9781259822674Author:Yunus A. Cengel Dr., Michael A. BolesPublisher:McGraw-Hill Education
- Control Systems EngineeringMechanical EngineeringISBN:9781118170519Author:Norman S. NisePublisher:WILEYMechanics of Materials (MindTap Course List)Mechanical EngineeringISBN:9781337093347Author:Barry J. Goodno, James M. GerePublisher:Cengage LearningEngineering Mechanics: StaticsMechanical EngineeringISBN:9781118807330Author:James L. Meriam, L. G. Kraige, J. N. BoltonPublisher:WILEY