Question

A car has an increasing speed at rate of 1.5m/s2 as it rounds a curve. What is the radius of curvature at a point when the speed of the car is 60kph and the magnitude of the total acceleration is 4m/s2?

Answer 1

The velocity of the car $= 60kph= 60* \frac{10^3}{3600}=16.67 m/s$

The normal acceleration $= a_n= \frac{v^2}{R}=\frac{16.67^2}{R}=\frac{277.77}{R}$

Total acceleration

$a= \sqrt{(a_T)^2+(a_n)^2}\\ 4= \sqrt{(1.5)^2+(\frac{277.77}{R})^2}\\ \implies R = 75 m$