1.)A motorist drives south at 30.0 m/s for 3.00 min, then turns west and travels

Question

1.)A motorist drives south at 30.0 m/s for 3.00 min, then turns west and travels at 25.0 m/s for 2.40 min, and finally travels northwest at 30.0 m/s for 1.00 min. For this 6.40 min trip, find the following values. Let the positive x axis point east.

(a) total vector displacement
m (magnitude)  ° south of west

(b) average speed
m/s

(c) average velocity
m/s (magnitude)  ° south of wes

2.)Suppose the position vector for a particle is given as a function of time by

(t) = x(t)î + y(t), with x(t) = at + b and y(t) = ct2 + d, where a = 1.50 m/s, b = 1.45 m,c = 0.124 m/s2, and d = 1.02 m.

(a) Calculate the average velocity during the time interval from t = 2.20 s to t = 3.90 s.

(b) Determine the velocity at t = 2.20 s.

Determine the speed at t = 2.20 s.
m/s

(a) Find the vector position of the particle at any time t (where t is measured in seconds).
(  t î +  t2) m

(b) Find the velocity of the particle at any time t.
(  î +  t ) m/s

(c) Find the coordinates of the particle at t = 7.00 s.
x =  m
y =  m

(d) Find the speed of the particle at t = 7.00 s.
m/s

5.)In a local bar, a customer slides an empty beer mug down the counter for a refill. The height of the counter is h. The mug slides off the counter and strikes the floor at distance d from the base of the counter.

(a) With what velocity did the mug leave the counter? (Use any variable or symbol stated above along with the following as necessary: g.)
vxi =

(b) What was the direction of the mug's velocity just before it hit the floor? (Use any variable or symbol stated above as necessary.)
=

below the horizontal

v

Explanation / Answer

1) r1 = (-30j)(3 x 60) = - 5400j m

r2 = (-25i)(2.40 x 60) = - 3600i m

r3 = (30 x 1 x 60)(-cos45i + sin45j)

r3 = - 1272i + 1272j m

r = r1 + r2 + r3

r = (-3600 - 1273)i + (-5400+ 1273j)

r = - 4873i - 4127j m

(A) magnitude = sqrt[(- 4873)^2 + (- 4127)^2]

= 6386 m

direction = tan^-1(4127 / 4873)

= 40 deg south of west

(b) average speed = total distance / time

= (5400 + 3600 + 1800) / (6.40 x 60)

= 28.1 m/s

(c) average velocity = displacement / time

magnitude = 6386/ (6.40 x 60)

= 16.6 m/s

direction = 40 deg south of west

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