#### Question

A particle moves in a circle of radius 1.0 cm at a speed given by *v* = 2.0 *t* where *v* is cm/s and *t* in seconds.

(a) Find the radial acceleration of the particle at *t* = 1 s.

(b) Find the tangential acceleration at *t* = 1 s.

(c) Find the magnitude of the acceleration at *t* = 1 s.

#### Solution

Speed is given as a function of time. Therefore, we have:*v* = 2*t*

Radius of the circle = *r* = 1 cm

At time *t *= 2 s, we get :

(a) Radial acceleration

\[\text{a} = \frac{\text{v}^2}{\text{r}} = \frac{2 {}^2}{1} = 4 \text{ cm/ s}^2\]

(b) Tangential acceleration

\[\text{a} = \frac{\text{dv}}{\text{dt}}\]

\[ = \frac{d}{\text{{dt}}}\left( 2t \right) = 2 \text{ cm/ s}^2\]

(c) Magnitude of acceleration

\[a = \sqrt{4^2 + 2^2}\]

\[ = \sqrt{20} \text{ cm/ s}^2\]

Is there an error in this question or solution?

Solution A Particle Moves in a Circle of Radius 1.0 Cm at a Speed Given by V = 2.0 T Where V is Cm/S and T in Seconds. Concept: Circular Motion.