Question

A car is moving along a circular path of radius $500m$ with a speed of $30m/s$. If at some instant, its speed increases at the rate of $2m/s^2$, then at that instant, the magnitude of resultant acceleration will be

• A. $4.7m/s^2$
• B. $3.8m/s^2$
• C. $3m/s^2$
• D. $2.7m/s^2$

Answer 1

The correct option is D $2.7m/s^2$

Let the tangential acceleration be $a_t$.
And let the centripetal acceleration be $a_c$.
Centripetal acceleration, $a_c=\frac{v^2}{r}$
$=\frac{(30{)}^2}{500}=1.8m/s^2$
$\therefore$ Resultant acceleration at the instant
$a=\sqrt{a_t^2+a_c^2}$
$=\sqrt{(1.8{)}^2+(2{)}^2}=2.7m/s^2$