Randall D. Knight — Kinematics in One Dimension: Problem Problem_73

When a 1984 Alfa Romeo Spider sports car accelerates at the maximum possible rate, its motion during the first 20 s is extremely well modeled by the simple equation \[ v_x^2 = \frac{2P}{m}t \] where \( P = 3.6 \times 10^4 \) watts is the car’s power output, \( m = 1200 \) kg is its mass, and \( v_x \) is in m/s. That is, the square of the car’s velocity increases linearly with time. a. Find an algebraic expression in terms of \( P \), \( m \), and \( t \) for the car’s acceleration at time \( t \). b. What is the car’s speed at \( t = 2 \) s and \( t = 10 \) s? c. Evaluate the acceleration at \( t = 2 \) s and \( t = 10 \) s.