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 = `\v_i` = 5 km/h = `\frac {5 ｘ1000 m}{1 ｘ3600 s}` = 1.39 m/s

Final Speed = `\v_f` = 7 km/h = `\frac {7 ｘ1000 m}{1 ｘ3600 s}` = 1.94 m/s

Acceleration of the cyclist = `\vec a` = ?


Solution:  

Acceleration:
The time rate of velocity is called acceleration `\vec a`. Mathematically:

`\vec a`  = `\frac {v_f - v_i}{t}` 

by putting values

`\vec a`  = `\frac {1.94 ms^{-1} - 1.39 ms^{-1}}{10 s}`

 `\vec 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 = `\v_i` = 0 m/s

Final Speed = `\v_f` = 20 km/h = `\frac {20 ｘ1000 m}{1 ｘ3600 s}` = 5.556 m/s

Acceleration of the car = `\vec a` = ?


Solution:  

We know that

`\vec a`  = `\frac {v_f - v_i}{t}` 

by putting values

`\vec a`  = `\frac {5.556 ms^{-1} - 0 ms^{-1}}{10 s}`

 `\vec 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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