A cyclist is cycling at a uniform speed of 8 m/s for 8 seconds.He then stops paddling and cycle comes to rest in next 10 seconds.Draw the velocity time graph and calculate: (i) the average retardation (ii) distance covered with uniform velocity (iii) distance covered with variable velocity (iv) average velocity of the cyclist ?

Asked by nisha_vini29 | 6th Jul, 2017, 11:44: AM

Expert Answer:

 
 
begin mathsize 12px style bold left parenthesis bold i bold right parenthesis space Retardation space is space the space slope space of space the space graph space line space BC equals space BD over DC space equals space fraction numerator 8 space straight m divided by straight s over denominator 10 space straight s end fraction space equals space 0.8 space straight m divided by straight s squared
bold left parenthesis bold ii bold right parenthesis space Distance space covered space with space uniform space velocity space equals space Area space of space the space rectangular space ABDE
space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space equals space AE space cross times space ED
space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space equals space 8 space straight m divided by straight s space cross times space 8 space straight s
space therefore space Distance space covered space with space uniform space velocity space equals space 64 space straight m
bold left parenthesis bold iii bold right parenthesis bold space space Distance space covered space with space variable space velocity space equals space Area space of space the space triangle space BDC
space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space equals space 1 half BD space cross times space DC equals space 1 half 8 space straight m divided by straight s space cross times space 10 space straight s
space therefore space Distance space covered space with space uniform space velocity equals space 40 space straight m
bold left parenthesis bold iv bold right parenthesis space Average space velocity space equals space fraction numerator Total space distance space covered over denominator Total space time end fraction
space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space equals space fraction numerator open parentheses 64 space plus space 40 close parentheses space straight m over denominator 18 space straight s end fraction
space therefore space Average space velocity space equals space 5.77 space straight m divided by straight s end style

Answered by Yashvanti Jain | 6th Jul, 2017, 01:44: PM