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find average velocity and average speed if the second hand of clock turns to 10 sec

Asked by pramilac968 6th January 2023, 9:02 PM
Answered by Expert
Answer:
Average velocity = displacement / time
 
Let r be the length of seconds hand in the clock.
 
In 10 seconds , second hand makes angular displacement 60o .
 
As shown in figure , displacement made by tip of second hand in 10 s is
 
displacement of tip of second hand = ( r cos60 ) begin mathsize 14px style i with hat on top end style  + ( r sin60-r) begin mathsize 14px style j with hat on top end style
displacement of tip of second hand = (r/2) begin mathsize 14px style i with hat on top end style + r [ (√3/2)-1 ] begin mathsize 14px style j with hat on top end style
average velocity of tip of second hand = displacement / time
 
average velocity of tip of second hand  = (r/20) begin mathsize 14px style i with hat on top end style + (r/10) [ (√3/2)-1 ] begin mathsize 14px style j with hat on top end style = r [ 0.05 begin mathsize 14px style i with hat on top end style - 0.013 begin mathsize 14px style j with hat on top end style ]
------------------------------------------------
 
Average speed = distance travelled / time
 
Distance travelled by tip of second hand in 10 seconds equals arc length AB as shown in figure
 
arc length AB = r × (begin mathsize 14px style straight pi end style/3 ) =
 
Average speed = r × (begin mathsize 14px style straight pi end style/30 ) = 0.105 r
Answered by Expert 7th January 2023, 12:19 AM
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