Question

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

• A. 5.5 m/s${}^2$
• B. 7.5 m/s${}^2$
• C. 9.5 m/s${}^2$
• D. 12.5 m/s${}^2$

Answer 1

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

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

Radial acceleration of the car at that instant, $a_r=\frac{v^2}{r}=\frac{{16}^2}{50}=5.12$ $m/s^2$

$\therefore$ Net acceleration of the car $a=\sqrt{a_r^2+a_t^2}=\sqrt{(5.12{)}^2+8^2}=9.5m/s^2$