Practice Problems Speed Velocity and Acceleration

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According to the rules of algebra we can rewrite the formula v d t in. two different ways, If we want to know how far a car going at 55 miles hour travels in 3. hours we write d vt 55 miles hour 3 hours 165 miles. If we want to know how long it will take this car to cover a distance. of 220 miles we write t d v 220 miles 55 miles hour 4. The units such as miles and hours are always carried along in. calculations and are treated like ordinary algebraic quantities. The result of every measurement has two parts a number and a unit. The number is the answer to How many and the unit is the answer to. Of what Unitsare standard quantities such as a second a meter a. mile The most widely used units today are those of the international. system abbreviated SI Syst me International d Unit s Examples. of SI units are the meter m for length the second s for time and the. kilogram kg for mass, The speed of an object is a scalar quantity It just tells us how fast the. object is moving but not in which direction it is headed The vector. quantity which specifies both the speed and the direction is called. the velocity Notation speed v velocity v, Turza s Physical Science Semester Exam Review Part Two. Forces and Motion Speed Velocity and Acceleration,Speed Velocity Acceleration Force. Sample Problems, A girl travels 20 miles on her bicycle The trip takes 2 hours Express her speed in miles hr.
1 First we identify the variables in our problem,distance d 20 miles. time t 2 hours, 2 We place the variables in their correct position in the speed formula. S 20 mi 2 hour, 3 Perform the calculation and express the resulting speed value with the appropriate unit. S 10 mi hr, A car starts from a stoplight and is traveling with a velocity of 10 m sec east in 20 seconds What is the. acceleration of the car, 1 First we identify the information that we are given in the problem.
vf 10 m sec,vo 0 m sec,time 20 seconds, 2 Then we insert the given information into the acceleration formula. a 10 m sec 0 m sec 20 sec, 3 Solving the problem gives an acceleration value of 0 5 m sec 2. Now try on your own, 1 What is the speed of a rocket that travels 9000 meters in 12 12 seconds 742 57 m s. 2 What is the speed of a jet plane that travels 528 meters in 4 seconds 132 m s. 3 How long will your trip take in hours if you travel 350 km at an average speed of 80 km hr 4 38 h. 4 How far in meters will you travel in 3 minutes running at a rate of 6 m s 1 080 m. 5 A trip to Cape Canaveral Florida takes 10 hours The distance is 816 km Calculate. the average speed 81 6 km h, 6 How many seconds will it take for a satellite to travel 450 km at a rate of 120 m s 3 750 s. 7 What is the speed of a walking person in m s if the person travels 1000 m in 20 minutes 0 80 m s. 8 A ball rolls down a ramp for 15 seconds If the initial velocity of the ball was 0 8 m sec and the. final velocity was 7 m sec what was the acceleration of the ball 0 413 m s. 9 A meteoroid changed velocity from 1 0 km s to 1 8 km s in 0 03 seconds What is the acceleration of. the meteoroid 26 7 km s, 10 A car going 50mph accelerates to pass a truck Five seconds later the car is going 80mph Calculate.
the acceleration of the car 6 mph s, 11 The space shuttle releases a space telescope into orbit around the earth The telescope goes from. being stationary to traveling at a speed of 1700 m s in 25 seconds What is the acceleration of. the satellite 68 m s, 12 A ball is rolled at a velocity of 12 m sec After 36 seconds it comes to a stop What is the. acceleration of the ball 0 33 m s, 13 How much force is needed to accelerate a truck with a mass of 2 000 kg at a rate of 3 m s 6 000 N. 14 A dragster in a race accelerated from stop to 60 m s by the time it reached the finish line The. dragster moved in a straight line and traveled from the starting line to the finish line in 8 0. sec What was the acceleration of the dragster 7 5 m s. 15 A 300 N force acts on a 25 kg object The acceleration of the object is 12 m s. Question 31,Back to Top, Question A certain force exerted for 1 2 seconds raises the speed of an object from 1 8 m s to 4 2 m s Later. the same force is applied for 2 seconds How much does the velocity change in 2 seconds. Answer Initial velocity u 1 8 m s,Final velocity v 4 2 m s.
Time t 1 2 seconds,First calculate acceleration, As the same force acts for the next two seconds the acceleration produced will be the same The final velocity in. the first case will now become the initial velocity We have to calculate the final velocity at end of 2 seconds. Acceleration a 2 m s2,Intial velocity u 4 2 m s t 2 s. Final velocity v,First equation of motion,Change in velocity in two seconds 8 2 4 2 4 m s. Question 32,Back to Top, Question Two blocks made of different metals identical in shape and size are acted upon by equal forces. which cause them to slide on a horizontal surface The acceleration of the second block is found to be 5 times that. of the first What is the ratio of the mass of second block to that of the first. Answer Let m1 and m2 be the mass of the first and second block respectively and a be the acceleration. Question 33,Back to Top, Question Brakes are applied on a car of mass 1000 kg moving with a velocity of 54 km h The car covers a.
distance of 50 m before coming to rest Calculate the force applied on the car. Answer Initial velocity u 54 km h, Final velocity v 0 because the car is brought to rest. Distance covered S 50 m, We have to calculate force applied i e F ma But we do not know the value of a Making use of III equation of. motion we get,Mass 1000 kg,Force 1000 x 2 25,Retarding force 2250 N. Question 34,Back to Top, Question A car of mass 800 kg moving at 108 km h is brought to rest over a distance of 15 m Find the. retarding force developed by the brakes of the car. Answer Initial velocity u 108 km hr,Final velocity v 0.
Distance covered S 15 m,III equation of motion Applying v2 u2 2aS. Mass of the car 800 kg,Retarding force 24000 N,Question 35. Back to Top, Question The velocity of a car of mass 1800 kg increases by 90 km h in 15 seconds Calculate the force. applied to increase the speed,Answer Mass of the car m 1800 kg. Force applied ma,Time t 15 seconds,Question 36,Back to Top.
Question What is the acceleration produced by a force of 12 Newton exerted on an object of mass 3 kg. Answer From Newton s second law of motion F ma,F 12 N mass m 3 kg. Question 37,Back to Top, Question What force would be needed to produce an acceleration of 4 m s 2 on a ball of mass 6 kg. Answer Acceleration a 4 m s2,Mass of the ball m 6 kg. Question 38,Back to Top, Question Why does a fielder in a cricket match move his hand backwards while making an attempt to catch the. Answer By moving the hand backwards the fielder increases the time of action of the force on his hands. When the time increases the force is reduced and the chances of the fielder getting hurt and dropping the ball is. Question 39,Back to Top, Question For how long should a force of 200 N act on a body of 20 kg so that it acquires a velocity of 100 m s.
Answer Time required to change the velocity of the body is to be calculated. Initial Velocity u 0,Final Velocity v 100 m s,The force should act on the body for 10 seconds. Question 40,Back to Top, Question A retarding force is applied for 10 seconds to stop 2000 kg heavy car moving with a uniform velocity. of 40 m s Calculate the retardation and the retarding force. Answer Time t 10 seconds,Final Velocity v 0 as the car comes to rest. Initial velocity u 40 m s,Mass of the car 2000 kg,Force required to stop the car ma. Retarding Force 8000 N,PROJECTILE, A projectile is any object that is cast fired flung heaved hurled pitched tossed or thrown This is an.
informal definition The path of a projectile is called its trajectory Some examples of projectiles include. a baseball that has been pitched batted or thrown, a bullet the instant it exits the barrel of a gun or rifle. a bus driven off an uncompleted bridge, a moving airplane in the air with its engines and wings disabled. a runner in mid stride since they momentarily lose contact with the ground. the space shuttle or any other spacecraft after main engine cut off MECO. A projectile is an object upon which the only force acting is gravity There are a variety of examples of. projectiles An object dropped from rest is a projectile provided that the influence of air resistance is. negligible An object that is thrown vertically upward is also a projectile provided that the influence of air. resistance is negligible And an object which is thrown upward at an angle to the horizontal is also a. projectile provided that the influence of air resistance is negligible A projectile is any object that once. projected or dropped continues in motion by its own inertia and is influenced only by the downward force. of gravity,Sample problems,Explore More, 1 A stone is thrown horizontally at a speed of 8 0m s from the edge of a cliff 80m in. height How far from the base of the cliff will the stone strike the ground. 2 A toy truck moves off the edge of a table that is 1 25m high and lands 0 40m from the. base of the table, a How much time passed between the moment the car left the table and the. moment it hit the floor, b What was the horizontal velocity of the car when it hit the ground.
3 A hawk in level flight 135m above the ground drops the fish it caught If the hawk s. horizontal speed is 20 0m s how far ahead of the drop point will the fish land. 4 A pistol is fired horizontally toward a target 120m away but at the same height The. bullet s velocity is 200m s How long does it take the bullet to get to the target How far. below the target does the bullet hit, 5 A bird traveling at 20m s wants to hit a waiter 10m below with his dropping see. image In order to hit the waiter the bird must release his dropping some distance before. he is directly overhead What is this distance, 6 Joe Nedney of the San Francisco 49ers kicked a field goal with an initial velocity. of 20m s at an angle of 60, a How long is the ball in the air Hint you may assume that the ball lands at same. height as it starts at, b What are the range and maximum height of the ball. 7 A racquetball thrown from the ground at an angle of 45 and with a speed. of 22 5m slands exactly 2 5s later on the top of a nearby building Calculate the. horizontal distanceit traveled and the height of the building. 8 Donovan McNabb throws a football He throws it with an initial velocity of 30m s at an. angle of 25 How much time passes until the ball travels 35m horizontally What is the. height of the ball after 0 5 seconds Assume that when thrown the ball is 2m above the. 9 Pablo Sandoval throws a baseball with a horizontal component of velocity of 25m s. After 2 seconds the ball is 40m above the release point Calculate the horizontaldistance it. has traveled by this time its initial vertical component of velocity and its initial angle of. projection Also is the ball on the way up or the way down at this moment in time. 10 Barry Bonds hits a 125m 450 home run that lands in the stands at an. altitude 30mabove its starting altitude Assuming that the ball left the bat at an angle. of 45 from the horizontal calculate how long the ball was in the air. 11 A golfer can drive a ball with an initial speed of 40 0m s If the tee and the green are. separated by 100m but are on the same level at what angle should the ball be driven. Hint you should use 2cos x sin x sin 2x at some point. 12 How long will it take a bullet fired from a cliff at an initial velocity of 700m s at an. angle 30 below the horizontal to reach the ground 200m below. 13 A diver in Hawaii is jumping off a cliff 45m high but she notices that there is an. outcropping of rocks 7m out at the base So she must clear a horizontal distance. of 7mduring the dive in order to survive Assuming the diver jumps horizontally what is. his her minimum push off speed, 14 If Monte Ellis can jump 1 0m high on Earth how high can he jump on the moon.
assuming same initial velocity that he had on Earth where gravity is 1 6 that of Earth s. 15 James Bond is trying to jump from a helicopter into a speeding Corvette to capture the. bad guy The car is going 30 0m s and the helicopter is flying completely horizontally. at 100m s The helicopter is 120m above the car and 440m behind the car How long must. James Bond wait to jump in order to safely make it into the car. 16 A field goal kicker lines up to kick a 44 yard 40m field goal He kicks it with an initial. velocity of 22m s at an angle of 55 The field goal posts are 3 meters high. a Does he make the field goal, b What is the ball s velocity and direction of motion just as it reaches the field goal. post i e after it has traveled 40m in the horizontal direction. 17 In a football game a punter kicks the ball a horizontal distance of 43 yards 39m On. TV they track the hang time which reads 3 9 seconds From this information calculate the. angle and speed at which the ball was kicked Note for non football watchers the projectile. starts and lands at the same height It goes 43 yards horizontally in a time of 3 9 seconds. Answers to Selected Problems,2 a 0 5s b 0 8m s,4 t 0 60s 1 8m below target. everyday usage acceleration is usually thought of as change in speed However it is important to remember that acceleration is change in velocity So even if an object is moving at a constant speed if it changes direction the object is accelerating The speed of an object is the rate at which it covers distance The

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