Final answer:
To find the curvature of the planar curve represented by the given quadratic equation, derive the equation, calculate the first and second derivatives, and substitute them into the formula for radius of curvature.
Step-by-step explanation:
The equation given, 4t^2 + 14.3t - 20 = 0, is a quadratic equation in the form at^2 + bt + c = 0, with a = 4, b = 14.3, and c = -20. To find the curvature of the planar curve, we can determine the radius of curvature using the formula R = (1 + (dx/dt)^2)^(3/2) / |d^2x/dt^2|, where x(t) represents the equation of the curve.
- Derive x(t) from the given quadratic equation.
- Calculate dx/dt and d^2x/dt^2 by taking the first and second derivatives of x(t).
- Substitute the values of dx/dt and d^2x/dt^2 into the formula for radius of curvature to find the curvature.