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KEY Kinematics Worksheet (Part 2) Name:___________________________ ___________ Date:______________ Mod:______________ Directions: Answer the following motion problems using the kinematic equations. Show your work and circle your final answer. 1. A speedboat increases in speed uniformly from 20m/s to 30m/s in a distance of 200m. What is the acceleration of the speedboat? 𝑣𝑓 2 = 𝑣𝑖 2 + 2𝑎𝑑 𝑚 𝑣𝑓 = 30 𝑠 𝑣𝑓 2 − 𝑣𝑖 2 𝑚 𝑎 = 𝑣𝑖 = 20 𝑠 2𝑑 2 2 𝑚 𝑎 =? (30 𝑠 ) − (20𝑚 𝑠) 𝑎= 𝑡 = 𝑥𝑥𝑥 2(200𝑚) 𝑑 = 200𝑚 𝑚 𝑎 = 1.25 𝑠2 2. A driver in a car traveling at a speed of 60 mi/hr sees a deer in the middle of the road 100m away. What is the minimum constant acceleration that is necessary for the car to stop? 60𝑚𝑖 5280𝑓𝑡 12𝑖𝑛 2.54𝑐𝑚 1𝑚 1ℎ𝑟 𝑥 𝑥 𝑥 𝑥 𝑥 = 26.82𝑚𝑠 𝑚 1ℎ𝑟 1𝑚𝑖 1𝑓𝑡 1𝑖𝑛 100𝑐𝑚 3600𝑠 𝑣𝑓 = 0 𝑠 𝑚 𝑣𝑖 = 26.82 𝑠 𝑎 =? 𝑡 = 𝑥𝑥𝑥 𝑑 = 100𝑚 𝑣𝑓 2 = 𝑣𝑖 2 + 2𝑎𝑑 𝑣𝑓 2 − 𝑣𝑖 2 𝑎= 2𝑑 2 2 − (0𝑚 ) (26.82𝑚 𝑠 𝑠) 𝑎= 2(100𝑚) 𝑚 𝑎 = −3.60 𝑠2 3. Julie is walking around a track at a 2m/s for some exercise. She then decides to start jogging so she accelerates at a rate of 0.5m/s² for 3 seconds. How far did Julie travel from the time she started to accelerate to the end of the 3 seconds? 𝑣𝑓 = 𝑥𝑥𝑥 1 𝑚 𝑑 = 𝑣𝑖 𝑡 + 2𝑎𝑡 2 𝑣𝑖 = 2 𝑠 𝑚 𝑎 = 0.5𝑠2 𝑡 = 3𝑠 𝑑 =? 𝑚 1 𝑚 𝑑 = (2 𝑠 ) (3 𝑠) + 2 (0.5𝑠2 ) (3 𝑠)2 𝑑 = 8.25𝑚 4. A rocket accelerates at a rate of 16.4m/s² for a distance of 50m. What is the velocity at the end of the 50m? 𝑣𝑓 2 = 𝑣𝑖 2 + 2𝑎𝑑 𝑣𝑓 = ? 𝑚 𝑣𝑓 = √𝑣𝑖 2 + 2𝑎𝑑 𝑣𝑖 = 0 𝑠 𝑚 𝑚 𝑣𝑓 = √2 (16.4 2 ) (50𝑚) 𝑎 = 16.4 2 𝑠 𝑡 = 𝑥𝑥𝑥 𝑑 = 50𝑚 Kinematics Worksheet (Part 2) Methacton High School Physics Department 𝑠 𝑚 𝑣𝑓 = 40.50 𝑠 1 5. A car can finish a 4.0x102 m race in 6.0 seconds. What is the minimum constant acceleration necessary? 𝑑 = 𝑣𝑖 𝑡 + 12𝑎𝑡 2 2(𝑑 − 𝑣𝑖 𝑡) 𝑣𝑓 = 𝑥𝑥𝑥 𝑎= 𝑚 𝑡2 𝑣𝑖 = 0 𝑠 2(400𝑚 − (0𝑚 𝑠 )(6.0𝑠)) 𝑎 =? 𝑎= 2 6.0𝑠 𝑡 = 6.0𝑠 𝑑 = 400𝑚 𝑚 𝑎 = 22.22 𝑠2 6. A car on a wet road can achieve an acceleration of only -1.00 m/s2 without sliding. Find the required stopping distance for a speed of 48km/hr. 48𝑘𝑚 1000𝑚 1ℎ𝑟 𝑚 𝑥 1𝑘𝑚 𝑥 3600𝑠 = 13.33𝑚𝑠 𝑣 = 0 1ℎ𝑟 𝑓 𝑠 𝑘𝑚 𝑣𝑖 = 48 ℎ𝑟 𝑣𝑓 2 = 𝑣𝑖 2 + 2𝑎𝑑 𝑣𝑓 2 − 𝑣𝑖 2 𝑑= 2𝑎 2 𝑚 2 (0 𝑠 ) − (13.33𝑚 𝑠) 𝑑= 2(−1.00𝑠𝑚2 ) 𝑚 𝑎 = −1.00𝑠2 𝑡 = 𝑥𝑥𝑥 𝑑 =? 𝑑 = 88.84𝑚 7. The normal reaction time for a human to respond to stimuli is around 0.60 seconds. A person driving a car is going 25.5 m/s at a constant speed when all of a sudden a deer jumps out onto the road. The person slams on his brakes and it takes 4.70 seconds to come to a complete stop. How far did the car travel once the driver saw the deer? 𝑑1 = 𝑣1 𝑡1 𝑚 𝑑1 = (25.5 𝑠 ) (0.60𝑠) 𝑑1 = 15.3𝑚 𝑚 𝑣𝑓2 = 0 𝑠 𝑚 𝑣𝑖2 = 25.5 𝑠 𝑎2 = 𝑥𝑥𝑥 𝑡2 = 4.70𝑠 𝑑2 = ? Reaction Time = Constant Velocity 𝑑1 Kinematics Worksheet (Part 2) Methacton High School Physics Department 𝑣𝑖2 + 𝑣𝑓2 𝑑2 = ( ) 𝑡2 2 𝑚 25.5 𝑠 + 0𝑚 𝑠 𝑑2 = ( ) 4.70 𝑠 2 𝑑𝑡𝑜𝑡𝑎𝑙= 𝑑1 + 𝑑2 = 15.30𝑚 + 59.93 𝑑𝑡𝑜𝑡𝑎𝑙 = 75.23𝑚 𝑑2 = 59.93 𝑚 𝑑2 Brake Applied = Deceleration 2