A rabbit runs in a parking lot such that its position vector is given by the function, which is defined as r(t) (3t^2+7) i + (2t-5) j, where r is in meters and t is in seconds. Find the magnitude and direction of the acceleration of the rabbit at t= 1 s
Acceleration (a)=d2r(t)/ dt2 =d/dt (6 ti + 2j)
a = 6i
At t= 1 sec
Acceleration (a) = 6 m/s2 j
The direction of acceleration is along positive y axis
A rabbit runs in a parking lot such that its position vector is given by the...
Suppose that the position vector of a particle is given by the following function of time: r = (6.0 + 2.0t^2)i + (3.0 - 2.0t + 3.0t^2)j where distance is measured in meters and time in seconds. (a) What is the instantaneous velocity vector at t=2.0 s? What is the magnitude of this vector? (b) What is the instantaneous acceleration vector? What are the magnitude and direction of this vector?
A girl operates a radio-controlled model car in a vacant parking lot. The girl’s position is at the origin of the xy coordinate axes, and the surface of the parking lot lies in the xy plane. She drives the car in a straight line so that the x coordinate is defined by the relation x(t) = 0.5t3 - 3t2 + 3t + 2 where x and t are expressed in meters and seconds, respectively. Determine when the velocity is 0...
The vector position of a particle varies in time according to the expression r = 8.20 i-5.60p j 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.) x m/s Determine the acceleration of the particle as a function of time. (Use any variable or symbol stated above as necessary.) X m/s2 (c) Calculate the particle's...
An object moves in the x-y-z space such that its position is defined by r (4t'i +3t +2t k) m, where t is in seconds. Determine the particle's velocity and acceleration when t 3 s.
(1 point) Given the acceleration vector a(t) = (-4 cos (2t))i + (-4 sin (2t))j + (-3t) k , an initial velocity of v (0) =i+ k, and an initial position of r (0)=i+j+ k, compute: A. The velocity vector v (t) = j+ . B. The position vector r(t) = j+ k
A particle moves so that its position vector is given by r -coswt i+sin wt j where w is constant a. Show that the velocityof the particle is perpendicular tor . b. Find the magnitude of acceleration in the direction of 2-h C. Show that dt
The position vector of a point which moves in the x-y plane is given by: r = (- 0.2 t4 + 1.8 t3 + 1.1 t2) i + (- 0.4 t4 - 1.2 t) j where r is in meters and t is in seconds. Determine the angle between the velocity v and the acceleration a when t = 1.7 sec.
The vector position of a particle varies in time according to the expression r-7.40 i-8.20t2 j 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.) m/s2 (c) Calculate the particle's position and velocity...
A particle's position ?⃗ as a function of time ? is given by ?⃗ (?)=??^3?̂ +(??−??4)?̂ . where a=5.00 m/s^3, b=3.00 m/s, and c=6.00 m/s^4. At t=2.45 s find: (e)The x-component of velocity. (f)The y-component of velocity. (g)The magnitude of the velocity vector. (h)The direction of the velocity vector. Your answer for this part should be in the range of -180 to 180 degrees. (i)The x-component of the acceleration. (j)The y-component of the acceleration. (k)The magnitude of the acceleration vector....
The position vector of a particle of mass 2.10 kg as a function of time is given by r with arrow = (6.00 î + 5.80 t ĵ), where r with arrow is in meters and t is in seconds. Determine the angular momentum of the particle about the origin as a function of time. k kg · m2/s 6.00 і + 5.80 tj. where r ıs in meters and t is in seconds. Determine the angular momentum of the...