Uniform Acceleration Problems Chapter 2: Linear Motion

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1 Name Date Period Uniform Acceleration Problem Chapter 2: Linear Motion INSTRUCTIONS: For thi homework, you will be drawing a coordinate axi (in math lingo: an x-y board ) to olve kinematic (motion) problem. You MUST draw a coordinate ytem for each problem that require you to ue one of the kinematic formula before you plug-n-chug the number. Lited to the right, are the four kinematic formula your learned about in chapter 5 and the one you will need to ue to olve the problem below. Definition of each of the variable you ee in the chart: v = Thi i the final velocity (or velocity of impact) (unit = m/) v 0 = Thi i the initial velocity. Ue a poitive (+) value if you initially throw omething up. Ue a negative value (-) if you initially throw omething down (unit = m/) If the initial velocity i zero (v 0 = 0), you can remove it from the equation. a = acceleration. When olving problem uing gravity, ubtitute g for a (remember g i a contant at -9.8 m/ 2 ) Thi i becaue gravity alway act downward. (unit = m/ 2 ) d = final ditance. In the problem involving object dropped, etc., d will repreent the diplacement in the y-direction. It i poitive (+) if the final poition i above where you threw it. It i negative (-) if the final poition of the object i below where your threw it. (unit = m) d 0 = initial ditance. Thi i where the object tarted. Thi value i very often = 0 (d 0 = 0). In thi cae, you can remove it from the equation. (unit = m) t = Thi the time the object i in motion. It i alway poitive. If you find it to be negative, then you did omething wrong! (unit = ) t 0 = Thi the initial time the object wa put in motion. Ye I know, you do not ee thi in any of the equation above. That i becaue it wa aumed in each that t 0 = 0, and wa therefore eliminated from the equation. REMEMBER we arrived at each of the equation above from our two favorite equation of average velocity and average acceleration! Motion Problem: When olving the kinematic motion problem, follow the following tep: ) Alway tart by writing down everything you know (the variable) and what they are aking you to find out (the unknown variable). 2) The next tep i to draw a viual repreentation of the problem (a picture) to help you keep track of what i happening and what you are looking for. You then need to draw a coordinate ytem (an x-y board) to determine (+) or (-) value for your variable. 3) Now chooe which equation fit your problem and plug in the value and olve for your unknown.

2 Example Problem: A car, traveling at 50 km/h, peed up at a contant rate of 5 m/ 2. What velocity i the car traveling 5.8 econd later? Step ) What do you know? v 0 = 50 km/h a = 5 m/ 2 t = 5.8 Make ure that the variable have common unit (ie. meter, kilometer, etc.) If not, you will firt need to convert. In the above problem we mut convert km/h to m/ for velocity. Refer back to your handout on converion if you need help. 3 km h x0 m 5 x0 =.4x0 3 h 3.6x0 km m What are you look- ing for? v =? (+) x direction Step 2) Draw a pic- ture and determine a coordinate ytem. v 0 =.4x0 m/ a = 5 m/ 2 t 0 = 0 v =? t = 5.8 Step 3) Now chooe which equation fit your problem and plug in the value and olve for your unknown. We know the value of v 0, a, and t. You are looking for v. After reviewing the table of equation, you hould have picked the equation: v = v 0 + at Now plug in value and do the math. Remember to include unit. m m v =.4x0 + 5 ( 5.8) = 2 4.3x0 Motion Problem: Show all work including: Picture (diagram), coordinate ytem, converion (if needed) and all known and/or unknown variable included. Make ure to include all unit when doing calculation and expre anwer in cientific notation. Quetion : A ball roll pat a mark on an incline at 0.50m/. If the ball ha a contant acceleration of 0.20m/ 2 what i it velocity 5.0 after it pae the mark? m v = 4.3x0 m 2

3 Quetion 2: A bu traveling at 40 km/h, peed up at a contant rate of 2.5 m/ 2. What velocity i the bu traveling 4.5 later? Quetion 3: A car accelerate from 0 m/ to 20 m/ in 5.0. How far doe the car travel in thi time? Quetion 4: A racing car accelerate at 4.5 m/ 2 from ret. What i the car velocity after it ha traveled 40 m? 3

4 Quetion 5: A car initially traveling at 5 m/ accelerate at a contant rate of 4.5 m/ 2 through a ditance of 45 m. How long doe it take the car to cover thi ditance? Quetion 6: A rock i dropped off a 50 m tall building. What i the impact velocity (final velocity)? Quetion 7: You are up on that 50 m tall building again. You drop a rock. How many econd doe it take to hit the ground? 4

5 Quetion 8: From that ame 50 m tall building, you throw a rock down at 25 m/. How many econd doe it take to hit the ground. Quetion 9: You are tanding outide of the claroom. Your friend i up on the roof (don t try thi at chool!). He i 5 m above you. You throw a tenni ball up to him with an initial velocity of 30 m/. He catche it a it goe up (in other word, the ball travel 5 m up). How fat i the ball going when it hit hi hand? Remember to include a + or ign in your final anwer. Quetion 0: Same cenario. Only thi time, your friend i lame and cannot catch the ball a it pae by him. The ball continue kyward. How high doe it go? (Hint: When it reache it highet point, it velocity will be 0 m/). 5

6 Quetion : Your friend look up and ee the ball coming back to him (remember, he mied it on it way up). Now what velocity will he catch it at. (In other word, he going to catch it on the way back down). (Hint: Thi i eay. Look at your anwer to #0, but think about a ign change). Quetion 2: Your friend decide to drop the ball on your head. He releae it from hi 5 m high perch. How long doe it take to hit the ground (in econd)? (He mie your head o you can ignore your peronal height). Quetion 3: Your friend decide to hurl another tenni ball at the ground at an initial velocity of 20 m/ toward the ground. At what velocity doe it hit the ground? 6