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

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