Chapter 04, Problem 011 The position of a (o)and te) tor range of (-180; 180). p

Question

Chapter 04, Problem 011 The position of a (o)and te) tor range of (-180; 180). partide mo ng in an xy plane is given by r-500t 3-600t)1+(6.00-200t4) with in meters and t in seconds. In unit-vector notation, calculate , and (e) a for t 2.00s. (d) What is the angle between t the positive direction of the x axis and a line tangent to the particle's path at t-2.00 ? Give your answer in the (a) Number Units (b) Number Units (e) Number Units (d) Number Units Click if you would like to Show Work for this g

Explanation / Answer

here,

r = ( 5 * t^3 - 6 * t) i + (6 - 2 t^4) j ...(1)

a)

for t = 2 s

r = ( 5 * t^3 - 6 * t) i + (6 - 2 t^4) j

r = ( 5 * 2^3 - 6 * 2) i + (6 - 2 * 2^4) j

r = 28 i m - 26 i m

b)

differentiating equation (1) for v

v = ( 15 * t^2 - 6) i + ( 6 - 8 * t^3) j ....(2)

for t = 2 s

v = 56 i - 58 j m/s

c)

differentiating equation (2) for a

a = 30 * t i - 24 * t^2 j

for t = 2 s

a = 60 i - 96 j m/s^2

d)

theta = arctan(-26 /28) = - 42.9 degree

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