Question

The MACH 5 car goes around a curve with a speed of 20.0 m/s experiencing a centripetalacceleration of 3.80 m/s2. What is the radius of the curve in meters? Round your answer correctly tothe first three places. No need for units for this problem.

Answer 1

Given data:

Velcoity of the car along the curve;

$v=20.0\text{ m/s}$

Centripetal acceleration of the car;

$a_c=3.80\text{ m/s}^2$

The centripetal acceleration is given as,

$a_c=\frac{v^2}{r}$

Here, r is the radius of the curve.

Rearranging the above equation to get an expression for radius of curve,

$r=\frac{v^2}{a_c}$

Substituting all known values,

$\begin{gathered} r=\frac{(20)^2}{3.80} \\ =105.26\text{ m} \\ \cong105\text{ m} \end{gathered}$

Therefore, the radius of the curve is 105 m.