Question #226696

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?

Expert's answer

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}\\\\\n4= \\sqrt{(1.5)^2+(\\frac{277.77}{R})^2}\\\\\n\\implies R = 75 m"

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