# A car travels along a horizontal circular curved road

A car travels along a horizontal circular curved road that has a radius of 600 m. If the speed is uniformly increased at a rate of 2000 km/$h^2$, determine the magnitude of the acceleration at the instant the speed of the car is 60 km/h.

#### Solution:

Let us first convert our units of measurement to our base units.

2000 km/$h^2$ = 0.1543 m/$s^2$

60 km/h = 16.67 m/s

Our tangential acceleration, $a_t$ is equal to 0.1543 m/$s^2$.

We now need to find the normal acceleration. It can be found using the following equation:

$a_n=\dfrac{v^2}{\rho}$

(Where $a_n$ is normal acceleration, $v$ is velocity, and $\rho$ is the radius of curved path)

$a_n=\dfrac{16.67^2}{600}$

$a_n=0.463$ m/$s^2$

The magnitude of acceleration can then be found using the following equation:

$a=\sqrt{(a_t)^2+(a_n)^2}$

$a=\sqrt{0.1543^2+0.463^2}=0.488$ m/$s^2$