In 10 seconds, a cyclist increases its speed from 5 km/h to 7km/h, while a car moves from rest to 20 km/h in same time. Calculate acceleration of each? Which has greater acceleration? 

Ans {0.055 m s⁻², 0.556 m s⁻², acceleration of the car is greater}


For Cyclist:

time = t = 10 s

Initial Speed = vivi = 5 km/h = 5ｘ1000m1ｘ3600s5ｘ1000m1ｘ3600s = 1.39 m/s

Final Speed = vfvf = 7 km/h = 7ｘ1000m1ｘ3600s7ｘ1000m1ｘ3600s = 1.94 m/s

Acceleration of the cyclist = →a→a = ?


Solution:  

Acceleration:
The time rate of velocity is called acceleration →a→a. Mathematically:

→a→a  = vf-vitvf−vit 

by putting values

→a→a  = 1.94ms-1-1.39ms-110s1.94ms−1−1.39ms−110s

 →a→a  = 0.055 m s⁻²-------Ans.1

Hence the cyclist has an acceleration of 0.055 m s⁻²




For Car:

time = t = 10 s

Initial Speed = vivi = 0 m/s

Final Speed = vfvf = 20 km/h = 20ｘ1000m1ｘ3600s20ｘ1000m1ｘ3600s = 5.556 m/s

Acceleration of the car = →a→a = ?


Solution:  

We know that

→a→a  = vf-vitvf−vit 

by putting values

→a→a  = 5.556ms-1-0ms-110s5.556ms−1−0ms−110s

 →a→a  = 0.556 m s⁻²-------Ans.2

Hence the car has an acceleration of 0.556 m s⁻²

By comparing Ans.1 and Ans.2 it is proved that Car has greater acceleration than a cyclist.


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