Question

A motorist drives south at 22.0 m/s for 3.00 min, then turns west and travels at 25.0 m/s for 2.20 min, and finally travels northwest at 30.0 m/s for 1.00 min. For this 6.20 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 west

Answer 1

here,

for t1 = 3 min = 180 s

v1 = 22 m/s (- j)

for t2 = 2.2 min = 132 s

v2 = 25 ( - i) m/s

for t3 = 1 min = 60 s

v3 = 30 m/s * ( - cos(45) i + sin(45) j)

v3 = (- 21.21 i + 21.21 j) m/s

a)

the total vector displacement , s = v1 * t1 + v2 * t2 + v3 * t3

s = (- 22 j) * 180 + ( -25 i ) * 132 + ( - 21.21 i + 21.21 j) * 60 m

s = - 4572.6 i m - 2687.4 j m

magnitude , |s| = sqrt(4572.6^2 + 2687.4^2) = 5303.67 m

direction , theta = arctan((-2687.4)/(4572.6)) = 30.44 degree SOuth of West

b)

average speed , v = (|v1*t1| + |v2*t2| + |v3 * t3|)/(t1 + t2 + t3)

v = ( 22 * 180 + 25 * 132 + 30 * 60)/(180 + 132 + 60)

v = 24.5 m/s

c)

magnitude of average velocity , |v'| = |s| /(t1 + t2 + t3) = 14.3 m/s

direction is same as displacement (30.44 degree SOuth of Wes)