4. + 410 points ! Previous Answers Ser529 6.P006.Wl. A car initiallytraveling ea

Question

4. + 410 points ! Previous Answers Ser529 6.P006.Wl. A car initiallytraveling eastward turns north by traveling in a circular path at uniform speed as in the figure below. The length of the arc ABC is 217 m, and the car completes the turn in 37.0 s 85. a) What is the acceleration when the car is at located at an angle of 35.0°7 Express your answer in terms of the unit vectors i and j First find the magnitude of the acceleration; then work out the components of the vector. ms i .024 Note that 217 is one quarter of the circumference of the circular path. m/sj (b) Determine the car's average speed. 36 m/s (c) Determine Its average acceleration during the 37.0-s interval. 0158x Does the x component of the velocity increase or decrease during this time interval? What does this tell you about the sign of the x component of the aceleration? ms 0.158

Explanation / Answer

length of the arc

circumference /4 = 217m

2*pi*r/4 = 217

r = 138.21 m

speed of car

v = arc length / time = 217/37 = 5.86 m/s ( answer of (b) )

as the car moving with constant velocity ,angular acceleration is zero .

normal acceleration an = v2 / r = 5.86*5.86 / 138.21 = 0.248 m/s^2

unit vector in the direction of normal acceleration

u = -cos35 i +sin35 j

vectorial representation of acceleration at point B

an = an .u = 0.248*( -cos35 i +sin35 j) = ( -0.203 i + 0.142 j ) m/s2 ( answer of (a) )

initial velocity v1 = 5.86 i m/s

final velocity v2 = 5.86 j m/s

average acceleration during given period

aavg = v2 -v1 / t = 5.86 j -5.86 i / 37

aavg = ( -0.158 i +0.158 j ) m/s2 ( answer of (c) )

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