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(III) The position of a particle moving in the xy plane is given by
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- The position r of a particle moving in an xy plane is given by ř seconds. In unit-vector notation, calculate (a) 7, (b) V , and (c) a for t = 3.00 s. (d) What is the angle between the positive direction of the x axis and a line tangent to the particle's path at t = 3.00 s? Give your answer in the range of (-180°; 180°). (4.00r3 – 1.00t)î + (5.00 – 1.00r4)j with 7 in meters and t in (a) Number i i Units (b) Number ît i Units i (c) Number i i Units (d) Number i Unitsarrow_forward0, y 0) 44. A projectile is launched from the point (x QC with velocity (12.0î + 49.0 j) m/s, at t = 0. (a) Make a table listing the projectile's distance |r| from the ori- gin at the end of each second thereafter, for 0 s I S 10 s. Tabulating the x and y coordinates and the compo- nents of velocity v and v will also be useful. (b) Notice that the projectile's distance from its starting point increases with time, goes through a maximum, and starts to decrease. Prove that the distance is a maximum when the position vector is perpendicular to the veloc- ity. Suggestion: Argue that if v is not perpendicular to f, then r|must be increasing or decreasing. (c) Determine the magnitude of the maximum displacement. (d) Explainarrow_forwardThe position of a particle moving in the xy plane varies with time, and its coordinates are given by the following expressions: x(t) = 4.00 m +r cos[(4.00/s)t] and y(t) = r sin[(4.00/s)t], where r = 2.00 m, and x and y will be in meters when t is in seconds. Determine the following for this particle. (a) speed of the particle at any time m/s (b) magnitude of the acceleration of the particle at any time m/s?arrow_forward
- 22)))At t = 0, a particle moving with constant acceleration in the xy plane has a velocity v = (3.00i-2.00j) m / s at its origin. At t = 3.00 s, the velocity of the particle is v = (9.00i + 7.00j) m / s. Find the acceleration of the particle?arrow_forward(b) A particle moves with position y = 2x , where x and y are in meters. The velocity in x direction is v, = 31² . Determine the velocity at time t = 5 s and write in unit vectors.arrow_forwardThe position vector of a moving particle in space at time t is given by the vector function r (t) = (3 - t)² i + (2t - 1) } + (3 - t)3/2 K Find the largest possible time when the particle reaches the speed of 4 units. Enter an integer or a fully reduced fraction such as 0 , 15 , 3/4 , etc.arrow_forward
- You are to make four straight-line moves over a flat desert floor, starting at the origin of an xy coordinate system and ending at the xy coordinates (-140 m, 30 m). The x component and y component of your moves are the following, respectively, in meters: (20 and 60), then (bx and -70), then (-20 and cy), then (-60 and -70). What are (a) component bx and (b) component cy? What are (c) the magnitude and (d) the angle (relative to the positive direction of the x axis) of the overall displacement?arrow_forwardThe position F of a particle moving in an xy plane is given by: F =(2.00"–5.00t)i +(6.00–7.00€*)} with ř in meters and t in seconds. (Note that this is an example where the units for the coefficients are ignored – don't let this distract you!) In unit vector notation, calculate: а). г b). V с). а for time t = 2.00 s. d). What is the angle between the positive direction of the x axis and a line tangent to the particle's path at t= 2.00 s?arrow_forwardA particle moves along a path, and its speed increases with time. (i) In which of the following cases are its acceleration and velocity vectors parallel? (a) when the path is circular (b) when the path is straight (c) when the path is a parabola (d) never (ii) From the same choices, in which case are itsacceleration and velocity vectors perpendicular everywhere along the path?arrow_forward
- A robotic vehicle, or rover, is exploring the surface of Mars. The stationary Mars lander is the origin of coordinates, and the sur-rounding Martian surface lies in the xy-plane. The rover, which we x = 2.0 m - 10.25 m > s22t2represent as a point, has x- and y-coordinates that vary with time:y = 11.0 m > s2t + 10.025 m > s32t3(a) Find the rover’s coordinates and distance from the lander at t = 2.0 s. (b) Find the rover’s displacement and average velocity vectors for the interval t = 0.0 s to t = 2.0 s. (c) Find a general S. Express expression for the rover’s instantaneous velocity vector vS at t = 2.0 s in component form and in terms of magnitude and vdirection. d) Find the instantaneous acceleration at t = 2.0 s. e) a1 , t=1sec a0 , t=0secarrow_forwardQuestion 5: The position vector of a particle moving in a circular path of radius R is given by the following expression T(t) = R[– sin(3t²)î+ cos(3t²)3] where B is a positive constant (i and j are the unit vectors corresponding to x and y axes in the two dimensional Cartesian Coordinate System, respectively). At time t = 4 secs., what is the ratio of magnitudes of the tangential acceleration and the centripetal acceleration, at where at and aț are the magnitudes of the tangential and the centripetal accelerations, respectively.arrow_forwardInitially, an object in uniform circular motion (assume clockwise motion) has a velocity vector given by v = (-3.00") î + (4.00"). If the radius of travel is 3.00 meters, determine the acceleration vector (in unit-vector notation) after 5.00 seconds have elapsed.arrow_forward
- Principles of Physics: A Calculus-Based TextPhysicsISBN:9781133104261Author:Raymond A. Serway, John W. JewettPublisher:Cengage LearningGlencoe Physics: Principles and Problems, Student...PhysicsISBN:9780078807213Author:Paul W. ZitzewitzPublisher:Glencoe/McGraw-Hill