An object moves in the x-y plane with a constant acceleration of 2i +3j meters per second squared. The object starts at the origin with some initial velocity. After four seconds (4 seconds) the velocity of the object is 2i + 8j meters per second. Determine the object’s initial velocity. Leave answer in i-j notation. Determine the position of the object at time, t = 4 seconds. Leave answer in i-j notation.

A rocket in free space generates a constant acceleration of (+8x^)[ms2](+8x^)[ms2]. If at t1=4t1=4 [s] the rocket has a velocity of v⃗ 1=−5x^v→1=−5x^ [m/s], what is the rocket's displacement between  t1t1 and t2=8t2=8 seconds? Select one: A.−20 [m] B. +256 [m] C. None of these are correct OR there is not enough information D.+472 [m] E.+44 [m] F.+216 [m] G.+59 [m] H.+27 [m] I. +21 [m] J. +108 [m] K.−40 [m] L.+64 [m]

As illustrated in the figure, a particle P moves on an x- y plane. In this motion, x( t) = 3 2 in meters and a(y) = 4 m /s?. It is also known that the position and velocity component along the y axis both vanish. Determine the speed as well as the x and y position of the particle at i = 3s. In your opinion, is the figure correct? If not, explain why and sketch a correction. Trajectory 60 a 50 40 30 P 20 10 50 100 150 200 250

Current Attempt in Progress In the figure, particle A moves along the line y = 31.4 m with a constant velocity of magnitude 2.89 m/s and directed parallel to the x axis. At the instant particle A passes the y axis, particle B leaves the origin with zero initial speed and constant acceleration a of magnitude 0.434 m/s2. What angle between a and the positive direction of the y axis would result in a collision? A B 0 X

A truck travels around a circular track. The position of the truck is described by the equations (400 · cos 0) m and 0 = (0.002 · t) rad, where t is in seconds. r = r = f@) Using cylindrical coordinates, a. Determine the truck's radial and transverse components of velocity at t = 4 s, v, and vo. b. Determine the truck's radial and transverse components of acceleration at t = 4 s, a, and ag.

The vector position of a particle varies in time according to the expression r = 9.00 î - 8.00t? ĵ where r is in meters and t is in seconds. (a) Find an expression for the velocity of the particle as a function of time, (Use any variable or symbol stated above as necessary.) m/s (b) Determine the acceleration of the particle as a function of time. (Use any variable or symbol stated above as necessary.) a = m/s2 (c) Calculate the particle's position and velocity at t = 3.00 s. ř = m/s Type here to search 近

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) =

The position of a dragonfly that is flying parallel to the ground is given as a function of time by 7 = [2.90 m + (0.0900 m/s²)t²] i – (0.0150 m/s³)t³ j. Part B At the time calculated in part (a), what is the magnitude of the acceleration vector of the insect? Express your answer with the appropriate units. xa μÅ Xb a = 0.062 a b X.10n m Submit Previous Answers Request Answer ?

A cyclist is travelling along a straight road. Graph 1 shows the cyclist's velocity during the first 32 s of his journey. 2. 30.0 25.0 20.0 15.0 10.0 5.0 0.0 0.0 5.0 10.0 15.0 20.0 25.0 30.0 35.0 Time (s) Graph 1 Sketch a graph of position on the vertical axis against time on the horizontal axis for the jourmey. a. b. Determine the average acceleration of the cyclist during: i. The first 16 seconds ii. Between 16 seconds and 24 seconds iii. Between 24 seconds and 32 seconds Calculate the average acceleration of the cyclist for the entire journey. d. Calculate the total distance that the cyclist travelled during the first 24 seconds. e. Draw a motion diagram that corresponds to Graph 1. Velocity (m/s)

An object is located initially at an origin. It has acceleration 3.00 m/s2, 90° and velocity 5.00 m/s, 0°. Determine the position (x, y) and the velocity (magnitude and direction) for times 1.00 s, 2.00 s and 3.00 s. Graph the position on an x-y coordinate plane for these times. Include the velocities and acceleration.