A Pebble is lodged into the outer edge of a spinning tire. The tire has a radius

Question

A Pebble is lodged into the outer edge of a spinning tire. The tire has a radius of 0.500 m and rotate g at a constant rate of 200 rev/min what is the magnitude of the Pebbles Velocity and acceleration? An unknown particles one dimensional is found to follow the function a_x = (10 - 1) m/s^2, where is in seconds. AT t = 0s its initial velocity and were found to be v_0 10mls what is the particles position at t = 10s? As you drive down a rood a night going 20m/s you are a deer which steps into the road 3sm in font Dr you takes you 0.50s to hit the brakes which cause you to decelerate at 10 m/s^2 How far away is the dear from you when you eventually come to a stop

Explanation / Answer

formula which relates angualr speed and linear speed is

v= rw

= 0.5 m ( 200 rev/min( 2pi rad/ rev * ( min/ 60 s)

=10.46 m/s

accleration is

a= r w^2

=  0.5 m ( 200 rev/min( 2pi rad/ rev * ( min/ 60 s) )^2

=219.1 m/s^2

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(b)

from the kinematic equation

sf- si= ut + 1/2 at^2

sf=  si+ ut + 1/2 at^2

=50 m+ (10 ) t + 1/2 ( 10-t) t^2

att= 10 s

sf = 50 m+ 10 (10) + 0

= 150 m

As per guide lines I worked first two problems kindly post remaining questions in the next post

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