simple vector calculus question?

acceleration = a(t)

velocity = v(t) = integral of a(t)

position = p(t) = integral of v(t)

Integrate a(t)dt to yield v(t). Recognize the constant of integration must satisfy the initial velocity of (i+2k).

Then integrate v(t) to yield the p(t). Recognize the constant of integration must satisfy the initial position of 0.

first one is easy, (x,y) = i + j so i is x componant and j is y componant so v = 6i -8j magazine of a vector is Sqrt ( x component^2 + y componant ^2) magazine v = sqrt (6^2 + (-8)^2 = sqrt (36 + sixty 4) = 10 c. using simalar triangels and trig you may artwork this one out, draw a diagram of the vector v such because of the fact the perimeters used to make the vector, this provide you a triangle. w would be interior the different direction alongside the hypotomuse and could be slightly longer, using the perimeters you be conscious of from the v vector you may calculate the attitude, then the triangle created by technique of vector w could have the comparable attitude and use trig to come to a decision the lengths. d. ( a million + xcomp of w , 5 + y comp of w) = very final factor, signs and indications are important