A car starts its motion and accelerates at a rate of 2 m/s². Find its velocity after covering a distance of 500 m.

Ans {44.7 m/s }


Data Given:


Initial Velocity of the car = `\vec v_i` = 0 m s⁻¹

Acceleration = `\vec a` = 2 m s⁻²

Distance travelled = 500 m


To Find:


Final velocity = `\vec v_f` = ?


Solution:  

According to the above-given data, the Final Velocity vf of the car can be calculated by using only the 3rd equation of motion.

Here we have

2aS  =  vf ² - vi ²

or

vf ²  = 2aS  + vi ²

By putting values

vf ²  =  2 (2 ms⁻²) (500m) +  (0 ms⁻¹) ² 

by simplifying we get

vf ²  =  2000 m² s⁻²

by taking square root on both sides 

`\sqrt{vf ²}` = `\sqrt{2000 m² s⁻²}`

by simplifying  we get 

vf   =  44.7 m s⁻¹ -------------Ans.


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