Suppose the position vector for a particle is given as a function of time by r(t) = x(t)î + y(t)ĵ, with x(t) = at + b and y(t) = ct² + d, where a = 1.10 m/s, b = 1.05 m, c = 0.124 m/s², and d = 1.16 m. (a) Calculate the average velocity during the time interval from t = 2.25 s to t = 3.85 s. = m/s
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- A particle is moving in three dimensions and its position vector is given by; r(t) = (4t² + 1.7t) î + (1.5t − 2.1)ĵ + (2.7t³ + 2t) k where r is in meters and t is in seconds. Determine the magnitude of the instantaneous velocity at t = 3s. Express your answer in units of m/s using one decimal place. Answer:A particle moving with an initial velocity v, = (10m/s)î and initial position 7, = (4m)î + (2m)j, undergoes an acceleration ở = 2t²î + 4ĵ in SI units. For t = 10 s; a) Calculate the velcoity v= vxI+ vy®. b) Calculate the position r= x+ y. c) What are the magnitudes of the velocity and the position vector of the particle? d) Find also the angle each vector is making with the x-axis at that time.Suppose that a particle begins its motion from the origin and meets the velocity (in m / s) given by: vx (t) = 2.50t vy (t) = 3.50√t. for t> 0 in seconds. Find the speed of the particle at t = 5.00 s What is the acceleration vector (in rectangular components) at t = 2.00 s ? Find the magnitude of the displacement between t = 0.00 s and t = 6.00 s
- Suppose the position vector for a particle is given as a function of time by r(t) = x(t)î + y(t)j, with x(t) = at + b and y(t) = ct + d, where a = 2.00 m/s, b = 1.15 m, c = 0.116 m/s2, and d = 1.08 m. (a) Calculate the average velocity during the time interval from t = 2.25 s to t= 3.80 s. m/s (b) Determine the velocity at t = 2.25 s. v = m/s Determine the speed at t = 2.25 s. m/sSuppose the position vector for a particle is given as a function of time by r(t) = x(t)î + y(t)j, with x(t) = at + b and y(t) = ct2 + d, where a = 2.00 m/s, b = 1.50 m, c = 0.132 m/s?, and d = 1.02 m. (a) Calculate the average velocity during the time interval from t = 2.25 s to t = 4.25 s. v = m/s (b) Determine the velocity at t = 2.25 s. v = m/s Determine the speed at t = 2.25 s. m/sAn object has an initial velocity of 29.0 m/s at 95.0° and an acceleration of 1.90 m/s2 at 200.0°. Assume that all angles are measured with respect to the positive x-axis. (a) Write the initial velocity vector and the acceleration vector in unit vector notation. (b) If the object maintains this acceleration for 12.0 seconds, determine the average velocity vector over the time interval. Express your answer in your unit vector notation.
- At time t = 0 a particle at the origin of an xyz-coordinate system has a velocity vector of Vo =i+ 12j - k. The acceleration function of the particle is a(t) = 16ti+j+ (cos 2t)k. Find the speed of the particle at time t = 1. Round your answer to two decimal places. Speed =At time t = 0, the position vector of a particle moving in the x-y plane is r = 4.62i m. By time t = 0.011 s, its position vector has become (4.84i +0.54j) m. Determine the magnitude Vay of its average velocity during this interval and the angle 0 made by the average velocity with the positive x-axis. Answers: Vav 0= i i m/sAt time t = 0, the position vector of a particle moving in the x-y plane is r = 5.80i m. By time t = 0.016 s, its position vector has become (6.08i + 0.42j) m. Determine the magnitude vay of its average velocity during this interval and the angle made by the average velocity with the positive x-axis. Answers: m/s Vav 0= i i
- Suppose the position vector for a particle is given as a function of time by r(t) = x(t)î + y(t)ĵ, with x(t) = at + b and y(t) = ct2 + d, where a = 1.10 m/s, b = 1.25 m, c = 0.123 m/s2, and d = 1.02 m. (a) Calculate the average velocity during the time interval from t = 1.85 s to t = 3.85 s. (b) Determine the velocity and speed at t = 1.85 s.Suppose the position vector for a particle is given as a function of time by r(t) = x(t)i + y(t)ĵ, with x(t) = at + b and y(t) = ct² +d, where a = 1.90 m/s, b = 1.50 m, c = 0.123 m/s², and d = 1.16 m. (a) Calculate the average velocity during the time interval from t = 1.90 s to t = 4.05 s. m/s V= (b) Determine the velocity at t = 1.90 s. m/s V= Determine the speed at t = 1.90 s. m/sSuppose the position vector for a particle is given as a func- tion of time by (1) = x(1)î + y(1)§, with x(1) y(t) = ct + d, where a = 1.00 m/s, b= 1.00 m, c= 0.125 m/s², and d = 1.00 m. (a) Calculate the average velocity during the time interval from t = 2.00 s to t= 4.00 s. (b) Determine the velocity and the speed at t = 2.00 s. at + b and