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Kinematics Practice ProblemsPractice A1. Heather and Matthew walk with an average velocity of 0.98 m/s eastward. If it takes them 34 min to walk to the store, what is their displacement?2. If Joe rides his bicycle in a straight line for 15 min with an average velocity of 12.5 km/h south, how far has he ridden?3. It takes you 9.5 min to walk with an average velocity of 1.2 m/s to the north from the bus stop to the museum entrance. What is your displacement?4. Simpson drives his car with an average velocity of 48.0 km/h to the east. How long will it take him to drive 144 km on a straight highway?5. Look back at item 4. How much time would Simpson save by increasing his average velocity to 56.0 km/h to the east?6. A bus travels 280 km south along a straight path with an average velocity of 88 km/h to the south. The bus stops for 24 min. Then, it travels 210 km south with an average velocity of 75 km/h to the south. a. How long does the total trip last? b. What is the average velocity for the total trip?Practice B1. As the shuttle bus comes to a sudden stop to avoid hitting a dog, it accelerates uniformly at ?4.1 m/s2 as it slows from 9.0 m/s to 0.0 m/s. Find the time interval of acceleration for the bus.2. A car traveling at 7.0 m/s accelerates uniformly at 2.5 m/s2 to reach a speed of 12.0 m/s. How long does it take for this acceleration to occur?3. With an average acceleration of ?1.2 m/s2, how long will it take a cyclist to bring a bicycle with an initial speed of 6.5 m/s to a complete stop?4. Turner’s treadmill runs with a velocity of ?1.2 m/s and speeds up at regular intervals during a half-hour workout. After 25 min, the treadmill has a velocity of ?6.5 m/s. What is the average acceleration of the treadmill during this period?5. Suppose a treadmill has an average acceleration of 4.7 × 10?3 m/s2. a. How much does its speed change after 5.0 min? b. If the treadmill’s initial speed is 1.7 m/s, what will its final speed be?Practice C1. A car accelerates uniformly from rest to a speed of 6.6 m/s in 6.5 s. Find the distance the car travels during this time.2. When Maggie applies the brakes of her car, the car slows uniformly from 15.0 m/s to 0.0 m/s in 2.50 s. How many meters before a stop sign must she apply her brakes in order to stop at the sign?3. A driver in a car traveling at a speed of 21.8 m/s sees a cat 101 m away on the road. How long will it take for the car to accelerate uniformly to a stop in exactly 99 m?4. A car enters the freeway with a speed of 6.4 m/s and accelerates uniformly for 3.2 km in 3.5 min. How fast (in m/s) is the car moving after this time?Practice D1. A car with an initial speed of 6.5 m/s accelerates at a uniform rate of 0.92 m/s2 for 3.6 s. Find the final speed and the displacement of the car during this time.2. An automobile with an initial speed of 4.30 m/s accelerates uniformly at the rate of 3.00 m/s2. Find the final speed and the displacement after 5.00 s.3. A car starts from rest and travels for 5.0 s with a constant acceleration of ?1.5 m/s2. What is the final velocity of the car? How far does the car travel in this time interval?4. A driver of a car traveling at 15.0 m/s applies the brakes, causing a uniform acceleration of ?2.0 m/s2. How long does it take the car to accelerate to a final speed of 10.0 m/s? How far has the car moved during the braking period?Practice E1. A car traveling initially at +7.0 m/s accelerates uniformly at the rate of +0.80 m/s2 for a distance of 245 m. a. What is its velocity at the end of the acceleration? b. What is its velocity after it accelerates for 125 m? c. What is its velocity after it accelerates for 67 m? 2. A car accelerates uniformly in a straight line from rest at the rate of 2.3 m/s2. a. What is the speed of the car after it has traveled 55 m? b. How long does it take the car to travel 55 m?3. A motorboat accelerates uniformly from a velocity of 6.5 m/s to the west to a velocity of 1.5 m/s to the west. If its acceleration was 2.7 m/s2 to the east, how far did it travel during the acceleration?4. An aircraft has a liftoff speed of 33 m/s. What minimum constant acceleration does this require if the aircraft is to be airborne after a take-off run of 240 m?5. A certain car is capable of accelerating at a uniform rate of 0.85 m/s2. What is the magnitude of the car’s displacement as it accelerates uniformly from a speed of 83 km/h to one of 94 km/h?Practice F1. A robot probe drops a camera off the rim of a 239 m high cliff on Mars, where the free-fall acceleration is ?3.7 m/s2. a. Find the velocity with which the camera hits the ground. b. Find the time required for it to hit the ground.2. A flowerpot falls from a windowsill 25.0 m above the sidewalk. a. How fast is the flowerpot moving when it strikes the ground? b. How much time does a passerby on the sidewalk below have to move out of the way before the flowerpot hits the ground? 3. A tennis ball is thrown vertically upward with an initial velocity of +8.0 m/s. a. What will the ball’s speed be when it returns to its starting point? b. How long will the ball take to reach its starting point?Practice G1. A baseball rolls off a 0.70 m high desk and strikes the floor 0.25 m away from the base of the desk. How fast was the ball rolling?2. A cat chases a mouse across a 1.0 m high table. The mouse steps out of the way, and the cat slides off the table and strikes the floor 2.2 m from the edge of the table. When the cat slid off the table, what was its speed?3. A pelican flying along a horizontal path drops a fish from a height of 5.4 m. The fish travels 8.0 m horizontally before it hits the water below. What is the pelican’s speed?4. If the pelican in item 3 was traveling at the same speed but was only 2.7 m above the water, how far would the fish travel horizontally before hitting the water below?Practice H1. In a scene in an action movie, a stuntman jumps from the top of one building to the top of another building 4.0 m away. After a running start, he leaps at a velocity of 5.0 m/s at an angle of 15° with respect to the flat roof. Will he make it to the other roof, which is 2.5 m shorter than the building he jumps from?2. A golfer hits a golf ball at an angle of 25.0° to the ground. If the golf ball covers a horizontal distance of 301.5 m, what is the ball’s maximum height?3. A baseball is thrown at an angle of 25° relative to the ground at a speed of 23.0 m/s. If the ball was caught 42.0 m from the thrower, how long was it in the air? How high did the ball travel before being caught?4. Salmon often jump waterfalls to reach their breeding grounds. One salmon starts 2.00 m from a waterfall that is 0.55 m tall and jumps at an angle of 32.0°. What must be the salmon’s minimum speed to reach the waterfall?Practice IConsider a projectile moving in a parabolic trajectory under constant gravitational acceleration. Its initial velocity has magnitude v0. Its launch angle (with the horizontal) is θ0.Calculate the time at the maximum height, Δtpeak, of the projectile.Calculate the time at the (horizontal) range, Δtmax, of the projectile.Calculate the (horizontal) range, R, of the projectile.Calculate the maximum height, H, of the projectile.Dr. Mel-Fu hits a ball at an angle of 25.0° to the ground (horizontal). If the ball covers a horizontal distance of 250.3 m, what is the ball’s maximum height?An airplane attempts to drop a bomb on a target. When the bomb is released, the plane is flying upward at an angle of 30° above the horizontal at a speed of 200 m/s, as shown below. At the point of release, the plane’s altitude is 2.0 km. The bomb hits the target.Determine the magnitude and direction of the vertical component of the bomb’s velocity at the point of release.Determine the magnitude and direction of the horizontal component of the bomb’s velocity at the point when the bomb contacts the target.Determine how much time it takes for the bomb to hit the target after it is released.At the point of release, what angle below the horizontal does the pilot have to look in order to see the target?This question concerns the motion of a car on a straight track; the car’s velocity as a function of time is plotted below.59436058420Describe what happened to the car at time t = 1s.How does the car’s average velocity between time t = 0 and t = 1s compare to the average velocity between times t = 1s and t = 5s?What is the displacement of the car from time t = 0 to time t = 7s?Plot the car’s acceleration during this interval as a function of time. Assume that the car begins at x = 0. ................
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