Assignment Submission Instructions For this assignment, you submit answers by qu

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Assignment Submission Instructions For this assignment, you submit answers by question parts. The number of submissions For the first problem part b, put a minus sign in front of youren atomiycian radial acceleration value. I failed to mention in class that formally inward is the negative direction in circular motion. When you calculate the speed In part c, use the magnitude of the radial acceleration under the radical. In addition parta of question 1 should be negative since the total acceleration vector points behind the radius. Since I did not put a minus sign in my answer, enter your tangential acceleration as a positive value. Two mistakes in one problem! you submit or change the answer. Assignment Scoring Your last submission is used for your score 1. -12.5 points My Notes Ask Your Teacher P4I A car is traveling in a circular path of 450 m circumference. At a particular instant the car has a total acceleration of 7.29 m/s 2 directed inward and 40.0 degrees behind the radius of the circular path. At this instant, a) what is the tangential acceleration of the car? b) what is the radial acceleration of the car? c) what is the speed of the car?

Explanation / Answer

A car is travelling in a circular path of 450 m circumference.

At a particular instant the car has a total acceleration of 7.29 m/s^2 directed inward and 40.0 degrees

behind the radius of the circular path.

At this instant what is the tangential acceleration of the car?

what is the radial acceleration of the car?

what is the speed of the car?

Given

the angle is 40 degrees

circumference is 2pr=450 m ==> r = 450/2pi m = 71.62 m

total acceleration is a= 7.29 m/s^2

first we calculate the speed  

from banking angle Tan theta = v^2/rg

tan 40 = v^2/(71.62*9.8)

v^2 = (71.62*9.8) (tan40)

v^2 = 588.94  

v =sqrt(588.94) m/s = 24.27 m/s

now the radial acceleration is a_r = v^2/r

a_r = 24.27^2/(71.62) m/s2 = 8.22 m/s2

and tangential acceleration is a_t

we know that total acceleration is a_T = sqrt(a_r^2+a_t^2)

7.29 = sqrt(8.22^2+a_t^2)

a_t = -3.8 m/s2

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