Question

If the tangential and centripetal accelerations are along a tangent and towards the centre, respectively, then the resultant acceleration will be :

• A. $a=a_t+a_c$
• B. $a=\sqrt{a_t^2+a_c^2}$
• C. $a=a_t-a_c$
• D. $a=a_c-a_t$

Answer 1

The correct option is B $a=\sqrt{a_t^2+a_c^2}$

The tangential acceleration $a_t$ acts along the tangent and the centripetal acceleration $a_c$ acts through the same point but towards the center. They both are aligned at ${90}^0$. Thus their vector addition yields $\sqrt{a_t^2+a_c^2}$