A point moves in the x,y plane. Position vector r(t), from the origin to the point, gives the location of the point at time, t. Unit vectors are i and j, each 1 unit long in the x and y directions respectively. Write answers assuming units of distance in meters and times in seconds.
Given: r(t)= (2 t^2 + 15) i - (8 t - 9) j
a. On an x,y axis system show r(0) and also r(3), then show vector D drawn
from the head of r(0) to the head of r(3) showing that r(0) + D = r(3).
b. From your drawing, find the magnitude and direction of the vector D.
c. Write the velocity vector, v(t), then write v(3) with polar coordinates.
d. Express the x coordinate as a function of time & make a qualitative graph
of x(t) then repeat for the y coordinate and make a qualitative graph of y(t).

Solution Summary

The position vector functions with unit vectors are examined. The coordinate as a function of time are given.

... Find its position vector r (t) at time t... Thus, the position vector, at time is given as: Problem: Find ... Problem: Find the unit tangent and normal vectors at the ...

... ground at a time t, r_pg(t). Express the position vector of the pebble in terms of R,w ,t , and the unit vectors x and/or y of the xy coordinate system shown. ...

... Force diagrams, vectors and equations of motion are examined. ... Since this is a vector equation, it must be true for ... with respect to time of the position vector r...

... solution answers various questions involving unit vectors in trigonometry ... The position vector is (4, 6)- (-1, 2)= (5 ... The vector that describes the motion of the ...

... Termsc anb ec alculated.w rite D own t he A ... where i, j, k are unit vectors along x, y and z axis ...Position vectors r' for each of the charges are as follows: ...

... A radio tower has a mass of 1200 kg and is supported in the vertical position by three cables from its top ... The basic location vectors are ... The vector along T1 is ...

...Vector V2 is 2.84 units long and points at 45 ... is the magnitude of the sum of these two vectors? ... the ground, measured from its initial position; d) eliminate ...

... a constant speed such that his position, measured from ... Where er , ez are the unit vectors in the ... vertical directions respectively (the radial unit vector is a ...

... The diagram below shows the position of the object when ... acting on the particle as a vector in terms ... It is better to use the polar unit vectors (tangential) and ...

... Express the answer by unit vectors. ... 1, a third charge qr = 1.0 pC is brought to position of P ... get the resultant electric field at E by getting the vector sum of ...