Question

A car is travelling at $20\text{m/s}$ on a circular road of radius $100\text{m}$ at an instant. If it's speed is increasing at the rate of $3{\text{m/s}}^2,$ it's acceleration (in ${\text{m/s}}^2$) at this instant is-

Answer 1

The acceleration has 2 components -tangential and centripetal
$a_c=\frac{v^2}{r}=\frac{20\times 20}{100}=\frac{400}{100}$
$a_c=4{\text{m/s}}^2$
$a_t=3{\text{m/s}}^2$
Net acceleration
$\sqrt{a_t^2+a_c^2}=\sqrt{(3{)}^2+(4{)}^2}$
$=\sqrt{(+16}=\sqrt{25}=5{\text{m/s}}^2$.