A particle travels in a circle of radius 1.0 cm with a speed given...

The speed of the particle is given by $v = 2.0 t$.

The tangential acceleration is the rate of change of speed:

$a_t = \dfrac{dv}{dt} = 2.0 \text{ cm/s}^2$

At $t = 1 \text{ s}$, the speed is:

$v = 2.0(1) = 2.0 \text{ cm/s}$

The radial (centripetal) acceleration is:

$a_r = \dfrac{v^2}{R} = \dfrac{(2.0)^2}{1.0} = 4.0 \text{ cm/s}^2$

The total acceleration is the vector sum of the tangential and radial accelerations:

$a = \sqrt{a_t^2 + a_r^2}$

$a = \sqrt{(2.0)^2 + (4.0)^2}$

$a = \sqrt{4.0 + 16.0} = \sqrt{20} \text{ cm/s}^2$