a particle is moving on a circular path of radius 1 m with 2m/s. If speed starts increasing at a rate of 2m/s^2 then the acceleration of particle is?

Dear student,

The acceleration has two components tangential acceleration and centripetal acceleration.
Tangential acceleration $a_t=2m/s^2$
Centripetal acceleration $a_r=\frac{v^2}{r}=\frac{{\left(2\right)}^2}{1}=4m/s^2$
Total acceleration is $a=\sqrt{{\left(2\right)}^2+{\left(4\right)}^2}=4.47m/s^2$

Regards.