Starting from rest at point A, you ride your motorcycle north (the direction) to

Question

Starting from rest at point A, you ride your motorcycle north (the direction) to point B 95.0 m away, increasing speed at a steady rate of 1.55 m/s2. You then gradually turn toward the east (the î direction) along a circular path of radius 45.0 m at constant speed from B to point C, until your direction of motion is due east at C. You then continue eastward, slowing at a steady rate of 1.1 m/s2 until you come to rest at point D.

(a) What is your average velocity and acceleration for the trip from A to D?
vavg = m/s

aavg = 0 m/s2

(b) What is your displacement during your trip from A to C?

m

(c) What distance did you travel for the entire trip from A to D?
  m

Starting from rest at point A, you ride your motorcycle north (the j direction) to point B 95.0 m away, increasing speed at a steady rate of 1.55 m/s You then gradually turn toward the east (the i direction along a circular path of radius 45.0 m at constant speed from B to point C, until your direction of motion is due east at C. You then continue eastward, slowing at a steady rate of 1.1 m/s until you come to rest at point D. (a) What is your average velocity and acceleration for the trip from A to D? avg 3.30 X m/s m/s avg (b) What is your displacement during your trip from A to C? 519.32 x m (c) What distance did you travel for the entire trip from A to D? 519.32 X m eBook

Explanation / Answer

from A to B

y = voy*t1 + (1/2)*ay*t1^2

95 = (1/2)*1.55*t2^2

t1 = 11.1 s

displacement rAB = 95 j

=============

from B to c

vB = sqrt(2*ay*y) = sqrt(2*1.55*95) = 17.2 m/s

time t2 = distance/time = (piR/2)/vBpi*R/(2*vB) = (pi*45)/(2*17.2)

t2 = 4.11 s

displacement r2 = R*cos45i + R*sin45 j

rBC = 45*cos45i + 45*sin45 j = 31.82i + 31.82 j

-----------

from C to D

displacement r3 = vB^2/(2*ax) i = 17.2^2/(2*1.1) = 134.47 i

rCD = vB*t3 + (1/2)*ax*t3^2

134.47 = (17.2*t) - (0.5*1.1*t^2)

134.47 = (17.2*t3) - (0.5*1.1*t3^2)

t3 = 15.7 s

================

(a)

average velocity

total displacemement r = r1 + r2 + r3

r = 95j + 31.82i + 31.82 j + 134.47 i

r = 166.29 i + 126.82 j

magnitude r = sqrt(166.29^2+126.82^2) = 209.13 m

Vavg = d/T = 209.13/(11.1+4.11+15.7) = 6.76 m/s

aavg = 0

===================

(b)

A to C

rAC = rA + rC = 95j + 31.82i + 31.82 j

rAC = 31.82 i + 126.82 j

rAC = sqrt(31.82^2+126.82^2) = 130.57 m <<<<<--answer

(c)

distance = 95 + (pi*45/2) + 134.47 = 300.1 m <<<------answer

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