I want solutions of these 6 questions with method.

SAMPLES OF PROBLEM-SOLVING QUESTIONS FOR TEST #2 YOU MUST SHOW YOUR WORK! (You may receive part-marks for showing work even if your calculations/answers are incorrect.) 1. Vibrations with frequency 6.00 x 10' Hz are established on a 1.33-m length of string that is clamped at both ends. The speed of waves on the string is 4.00 x 10 m/s. How far from either end of the string does the first node occur? Show your steps clearly and give your answer rounded off to the appropriate number of significant digits with the correct unit(s). (4 marks) Ans: 0.33 m 2. A car traveling along a road begins accelerating with a constant acceleration of 1.5 m/s in the direction of motion. After traveling 392 m at this acceleration, its speed is 35 m/s. Determine the speed of the car when it began accelerating. Show your steps clearly and give your answer rounded off to the appropriate number of significant digits with the correct unit(s) (3 marks) Ans: 7.0 m/s 3. A car traveling at 20 m/s follows a curve in the road so that its centripetal acceleration is 5 m/s". What is the radius of the curve? Show your steps clearly and give your answer rounded off to the appropriate number of significant digits with the correct unit(s). (3 marks) Ans: 80 m 4. A fan rotating with an initial angular velocity of 1000 rev/min is switched off. In 2 seconds, the angular velocity decreases to 200 rev/min. Assuming the angular acceleration is constant, how many revolutions does the blade undergo during this time? Show your steps clearly and give your answer rounded off to two significant digits with the correct unit(s). (3 marks) Ans: 20 5. A 1.0-kg block oscillates with a frequency of 10. Hz at the end of a certain spring. The spring is then cut into two halves. The 1.0-kg block is then made to oscillate at the end of one of the halves. What is the frequency of oscillation of the block? Show your steps clearly and give your answer rounded off to the appropriate number of significant digits with the correct unit(s). (4 marks) Ans: 14 Hz 6. At what separation will two charges, cach of magnitude 6.0 HC, exert a force of 0.70 N on each other? Show your steps clearly and give your answer rounded off to the appropriate number of significant digits with the correct unit(s). (3 marks) Ans: 0.68 m