Question

A car is travelling along a circular curve that has a radius of $50$ m. If its speed is $16$ m/s and is incrcasing uniformly at $8m/s^2.$ Determine the magnitude of its acceleration at this instant.

• A. $7.5m{s}^{-2}$
• B. $8.5m{s}^{-2}$
• C. $9.5m{s}^{-2}$
• D. $9.8m{s}^{-2}$

Answer 1

The correct option is C $9.5m{s}^{-2}$

Given : $r=50$ m $a_t=8$ $m/s^2$ $v=16$ $m/s$

Centripetal acceleration $a_r=\frac{v^2}{r}=\frac{(16{)}^2}{50}=5.12$ $m/s^2$

$\therefore$ Total acceleration $a=\sqrt{a_r^2+a_t^2}=\sqrt{(5.12{)}^2+8^2}=\sqrt{90.2}=9.5$ $m/s^2$