Model: Model the flea as a particle. Both the initial acceleration phase and the free-fall phase have constant acceleration, so use the kinematic equations. Model: Model each of the animals as a particle and use kinematic equations. We can solve for the position and the velocity at t2 , the end of the first phase. From t2 to t3 the gazelle moves at a constant speed, so we can use the equation for uniform motion to find its final position.
The gazelle is just a few meters ahead of the cheetah when the cheetah has to break off. Assess: The numbers in the problem statement are realistic, so we expect our results to mirror real life. The speed for the gazelle is close to that of the cheetah, which seems reasonable for two animals known for their speed. And the result is the most common occurrence—the chase is very close, but the gazelle gets away.
Solve: a There are three parts to the motion. The maximum altitude is y2. The maximum altitude is Assess: In reality, friction due to air resistance would prevent the rocket from reaching such high speeds as it falls, and the acceleration upward would not be constant because the mass changes as the fuel is burned, but that is a more complicated problem.
Model: We will model the rocket as a particle. Air resistance will be neglected. Model: We will model the lead ball as a particle and use the constant-acceleration kinematic equations. Note that the particle undergoes free fall until it hits the water surface. The negative sign shows the direction of the displacement vector.
Assess: A depth of about 60 ft for a lake is not unusual. Model: The elevator is a particle moving under constant-acceleration kinematic equations. This is comparable to the time of 45 s for the entire trip as obtained above.
Model: The car is a particle moving under constant-acceleration kinematic equations. Solve: This is a three-part problem. First the car accelerates, then it moves with a constant speed, and then it decelerates.
Model: Santa is a particle moving under constant-acceleration kinematic equations. Visualize: Note that our x-axis is positioned along the incline. Solve: a Ann and Carol start from different locations at different times and drive at different speeds. But at time t1 they have the same position. It is important in a problem such as this to express information in terms of positions that is, coordinates rather than distances.
Model: Model the ice as a particle and use the kinematic equations for constant acceleration. Set the x-axis parallel to the ramp. This is true for both angles as the answer is independent of the angle.
Assess: We will later learn how to solve this problem in an easier way with energy. Model: We will use the particle model and the kinematic equations at constant-acceleration. He is in jail. Assess: Bob is driving at approximately mph and the stopping distance is of the correct order of magnitude. Model: We will use the particle model with constant-acceleration kinematic equations. That is, the puck goes through a displacement of 8. Since the end of the ramp is 8.
The units check out. Model: The ball is a particle that exhibits freely falling motion according to the constant-acceleration kinematic equations. Solve: The reaction time is 1. This is physically impossible for the Alfa Romeo. Model: Both cars are particles that move according to the constant-acceleration kinematic equations.
Solve: We will first calculate the time tC1 the cat takes to reach the window. The dog has exactly the same time to reach the cat or the window. The cat is safe. Model: Jill and the grocery cart will be treated as particles that move according to the constant-acceleration kinematic equations.
Model: The watermelon and Superman will be treated as particles that move according to constantacceleration kinematic equations. The speed of the watermelon as it passes Superman is. Note that the negative sign implies a downward velocity. Assess: A speed of mph for the watermelon is understandable in view of the significant distance m involved in the free fall. Model: Treat the car and train in the particle model and use the constant acceleration kinematics equations.
Solve: In the particle model the car and train have no physical size, so the car has to reach the crossing at an infinitesimally sooner time than the train. Crossing at the same time corresponds to the minimum a1 necessary to avoid a collision. The time it takes the train to reach the intersection can be found by considering its known constant velocity. Now find the distance traveled by the car during the reaction time of the driver.
However, you should not try this yourself! Always pay attention when you drive! Train crossings are dangerous locations, and many people lose their lives at one each year.
Model: Model the ball as a particle. Since the ball is heavy we ignore air resistance. Making all these substitutions leaves. So we expect a graph of h vs. Solve: First look at a graph of height vs. It would be difficult to analyze.
Even though the point 0, 0 is not a measured data point, it is valid to add to the data table and graph because it would take zero time to fall zero distance. However, the theory has guided us to expect that a graph of height vs. First we use a spreadsheet to square the fall times and then graph the height vs.
We also see that the intercept is a very small negative number which is close to zero, so we have confidence in our model. The fit is not perfect and the intercept is not exactly zero probably because of uncertainties in timing the fall. Assess: The free-fall acceleration on Planet X is a little bit smaller than on earth, but is reasonable. It is customary to put the independent variable on the horizontal axis and the dependent variable along the vertical axis.
Web icon An illustration of a computer application window Wayback Machine Texts icon An illustration of an open book. Books Video icon An illustration of two cells of a film strip. Video Audio icon An illustration of an audio speaker. Audio Software icon An illustration of a 3. Software Images icon An illustration of two photographs.
Images Donate icon An illustration of a heart shape Donate Ellipses icon An illustration of text ellipses. Solutions manual for students to accompany Physics for scientists and engineers, third edition, by Paul A.
Absent-mindedly he missed his exit and stopped after one hour of driving at another rest area 20 miles south of El Dorado. After waiting there for one hour, he drove back very slowly, confused and tired as he was, and reached El Dorado two hours later.
Visualize: The bicycle move forward with an acceleration of 1. Thus, the velocity will increase by 1. Visualize: The rocket moves upward with a constant acceleration a. Solve: a 6. Solve: a 8.
Solve: a This height is approximately 8 times my height. Solve: I typically take 15 minutes in my car to cover a distance of approximately 6 miles from home to campus. Solve: My barber trims about an inch of hair when I visit him every month for a haircut. Model: Represent the Porsche as a particle for the motion diagram. Assume the car moves at a constant speed when it coasts. Visualize: 1. Model: Represent the jet as a particle for the motion diagram.
Model: Represent the wad as a particle for the motion diagram. Model: Represent the speed skater as a particle for the motion diagram. Model: Represent Santa Claus as a particle for the motion diagram. Model: Represent the motorist as a particle for the motion diagram.
Model: Represent the car as a particle for the motion diagram. Model: Represent Bruce and the puck as particles for the motion diagram.
Model: Represent the cars of David and Tina and as particles for the motion diagram. Solve: Isabel is the first car in line at a stop light. When it turns green, she accelerates, hoping to make the next stop light m away before it turns red. The car decelerates as it coasts up the hill. At the top, the road levels and the car continues coasting along the road at a reduced speed. At the bottom of the m slope the terrain becomes flat and the skier continues at constant velocity. Solve: A ball is dropped from a height to check its rebound properties.
Solve: Two boards lean against each other at equal angles to the vertical direction. A ball rolls up the incline, over the peak, and down the other side.
The driver maintains this constant speed for the entire length of the tunnel that takes the train a time of 20 s to traverse. Find the length of the tunnel. If the blocks are 50 m long, how long does it take Sue to drive from 3rd Street to 5th Street?
Solve: a b Jeremy has perfected the art of steady acceleration and deceleration. From a speed of 60 mph he brakes his car to rest in 10 s with a constant deceleration. Then he turns into an adjoining street. Starting from rest, Jeremy accelerates with exactly the same magnitude as his earlier deceleration and reaches the same speed of 60 mph over the same distance in exactly the same time.
Solve: a b A coyote A sees a rabbit and begins to run toward it with an acceleration of 3. At the same instant, the rabbit B begins to run away from the coyote with an acceleration of 2. The coyote catches the rabbit after running 40 m. How far away was the rabbit when the coyote first saw it?
Similarly, the largest area will correspond to the larger length and the larger width. There are cm in 1 m. Model: In the particle model, the car is represented as a dot. Solve: a Time t s Position x m b 0 10 20 30 40 50 60 70 80 90 0 1. Solve: Susan enters a classroom, sees a seat 40 m directly ahead, and begins walking toward it at a constant leisurely pace, covering the first 10 m in 10 seconds.
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