The velocity-time relation of an electron starting . . .

Question : The velocity-time relation of an electron starting from rest is given by v=kt, where k=2m/s². The distance traversed in first 3s is _________ (in m).

Doubt by Suhani 

Solution : 

v=kt
k=2 m/s²

v=2t
dx/dt = 2t
dx=2tdt

Integrating both sides within proper limits


Hence, the distance traversed in first 3s is equal to 9 m.