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 = 1.40 m/s, b = 1.50 m, c = 0.117 m/s², and d = 1.12 m. (a) Calculate the average velocity during the time interval from t = 2.15 s to t = 4.10 s. v = m/s (b) Determine the velocity at t = 2.15 s. v = m/s Determine the speed at t = 2.15 s. m/s

Given the displacement vector ? =[3.1?2, 2.0?, 0]:(a) what is the position of the object at time? = 2.1 ? assuming the object started at theorigin?(b) what is the distance the object has traveled at? = 2.1 ??(c) what is the velocity of the object as a functionof time?(d) what is the velocity of the object at ? = 0, ? =2.1 ? and ? = 4.2 ??(e) what is the speed of the object at the timesgiven in part (d). Are the speed evenly spaced?Would you expect this? Why or why not?(f) what is the acceleration of the object at? = 0, ? = 2.1 ? and ? = 4.2 ??

Suppose that the position vector for a particle is given as a function of time by (t) = x(t)î + y(t)ĵ, with x(t) = at + b and y(t) = ct2 + d, where a = 2.00 m/s, b = 1.05 m, c = 0.117 m/s2, and d = 1.16 m. (a) Calculate the average velocity during the time interval from t = 2.05 s to t = 3.85 s.   =       m/s (b) Determine the velocity at t = 2.05 s.   =       m/s Determine the speed at t = 2.05 s. m/s

The figure shows the y-position (in blue) of a particle versus time. y (m) 20 16 12 Need Help? 8 4 0 1 2 3 4 (a) What is the average velocity of the particle during the time interval t = 0.50 s to t = 4.50 s? (Express your answer in vector form.) m/s m/s 5 (b) Using the tangent to the curve (shown as the orange line in the figure), what is the instantaneous velocity of the particle at t = 1.50 s? (Express your answer in vector form.) -t (s) Read It (c) At what time is the velocity of the particle equal to zero? S

The velocity of a particle moving in the xy plane is given by = ( 5.50 r- 5.00 P)i + 9.00). with V in meters per second and t- 0l in seconds. At t-1.40 s and in unit-vector notation, what are lal the xcomponent and (bi the y component of the acceleration? ) When of ever) is the acceleration zero? (d) At what positive time does the speed eoual 100 ms? 1 unit (al Number } unit This anwer hannunts degrees Number O Number Unit (d) Number Unit Hint Pa GO Tutorial Save for Later times Attempts: unlimited Smit Arr

​Suppose the position vector for a particle is given as a function of time by , with x(t) = at + b and y(t) =ct2 + 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 = 1.00 s to t = 4.00 s. (b) Determine the velocity and the speed at t = 3.00 s. (c) Determine the acceleration at t = 3.00 s.

Use the given acceleration function and initial conditions to find the velocity vector v(t), and position vector r(t). Then find the position at time t = 3. a(t) = 8i + 4k v(0) = 5j, r(0) = 0 v(t) = r(t) = r(3) =

A puck is moving on an air hockey table. Relative to an x, y coordinate system at time t = 0s, the x components of the puck's initial velocity and acceleration are vox = +7.2 m/s and ax = +1.1 m/s². They components of the puck's initial velocity and acceleration are Voy=+3.6 m/s and ay = -1.5 m/s². Find (a) the magnitude v and (b) the direction of the puck's velocity at a time of t = 0.50 s. Specify the direction relative to the +x axis. (a) v = i (b) 0= degrees the +x axis

The position vector 4.70t|i+ [et + ft2 locates a particle as a function of time t. Vector is in meters, t is in seconds, and factors e and f are constants. The figure gives the angle e of the particle's direction of travel as a function of time (0 is measured from the positive direction of the x axis). What are (a) factor e and (b) factor f, including units? 20° 0° 10 20 -20° t (s) (a) Number Units (b) Number Units

A particle leaves the origin with an initial velocity 3.00î m/s and a constant acceleration ở -1.00î – 0.50ĵ m/s². When it reaches its maximum x coordinate, what are its (a) velocity and (b) position vector?