Question

A motorist drives south at 24.0 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 in m (magnitude) ° south of west(b) average speed (m/s)(c) average velocity in m/s (magnitude) ° south of west

Answer 1

Answer:

magnitude m = 5440.26 M

average speed is = 25.05 m/s

average velocity = 14.62 m/s

Explanation:

given data

speed v1 = 24 m/s

time t1 = 3 min = 180 s

speed v2 = 25 m/s

time t2 = 2.2 min = 132 s

speed v3 = 30 m/s

time t3 = 1 min = 60 s

total time = 6.2 min = 372 s

to find out

displacement in m  and average speed and  average velocity

solution

so we find here displacement

displacement = vt    .............1

so

displacement 1 = 24 × 180 =  4220 m south = -4220 j   ..........2

displacement 2 = 25 × 132 = 3300 m west = -3300 i     ...........3

distance 3 = 30 × 60 =  1800 m

displacement   = 1800 cos45 -i + 1800 cos45 j

displacement   = -1272.79 i + 1272.79 j                             .............4

so total displacement D =  equation 2 + equation 3 + equation 4

total displacement D =  -4220 j -3300 i -1272.79 i + 1272.79 j

total displacement D =  -2947.21 j - 4572.79 i

so magnitude m = √(-2947.21)² + (-4572.79)² )

so magnitude m = 5440.26 M

and

average speed is = total distance / time

average speed is = (4220 + 3300+ 1800 ) / 372

average speed is = 25.05 m/s

and

average velocity = total displacement / time

average velocity = 5440.26 / 372

average velocity = 14.62 m/s