The components of a position vector of a particle moving in the plane are components 2 times t squared, cosine of t . What is the distance traveled by the particle from t = 0 to t = π?

Question

The components of a position vector of a particle moving in the plane are  . What is the distance traveled by the particle from t = 0 to t = π?



Type your answer in the space below and give 3 decimal places. If your answer is less than 1, place a leading "0" before the decimal point (ex: 0.482)

Answer 1

Distance traveled by particle d = ∫₀^π√(x'² + y'²)dt = ∫₀^π _√(4t)²+ (-sin(t))²dt = ∫₀^π(16t² + sin²t)^1/2dt = 19.89;

We used TI-84 to evaluate this integral