40. The spring in a dart gun has a spring constant of 20.0 N/m. The spring is compressed 8.00 x 10-2 m from its equilibrium position and used to launch a 1.00 x 10-2 kg plastic dart. Ignoring friction, what is the dart’s speed as it leaves the gun?A. 0.0640 m/sB. 3.58 m/sC. 7.21 m/sD. 12.8 m/s **Unit 5: Energy, Work, and Power****Question 40:**The spring in a dart gun has a spring constant of 20.0 N/m. The spring is compressed 8.00 x 10⁻² m from its equilibrium position and used to launch a 1.00 x 10⁻² kg plastic dart. Ignoring friction, what is the dart’s speed as it leaves the gun?**Options:**A. 0.0640 m/s B. 3.58 m/s C. 7.21 m/s D. 12.8 m/s **Unit 5: Energy, Work, and Power****Question 40:**The spring in a dart gun has a spring constant of 20.0 N/m. The spring is compressed 8.00 x 10⁻² m from its equilibrium position and used to launch a 1.00 x 10⁻² kg plastic dart. Ignoring friction, what is the dart’s speed as it leaves the gun?- **A.** 0.0640 m/s- **B.** 3.58 m/s- **C.** 7.21 m/s- **D.** 12.8 m/s

Given data: Spring constant (k) = 20.0 N/m Compression in spring (x) = 8.00 × 10-2 m Mass of dart (m) = 1.00 × 10-2 kg Required: The speed (v) of plastic dartAccording to conservation of energy The total energy of the spring-dart system remains constant. Gain in kinetic energy of dart = loss in potential energy of spring ∆KE = ∆SPE12mv2 = 12kx2v = kx2m=20.0N/m8.00×10-2 m2 1.00×10-2 kg= 3.5777 m/s≈ 3.58 m/s The speed of the dart as it leaves the gun is 3.58 m/s Hence, the correct answer is option (B)