Skip to main content
Pearson+ LogoPearson+ Logo
Ch 02: Motion Along a Straight Line
Back
Previous problem
Next problem
All textbooksYoung & Freedman Calc 14th EditionCh 02: Motion Along a Straight LineProblem 2

Chapter 2, Problem 2

High-speed motion pictures (3500 frames/second) of a jumping, 210–μg flea yielded the data used to plot the graph in Fig. E2.54. (See 'The Flying Leap of the Flea' by M. Rothschild, Y. Schlein, K. Parker, C. Neville, and S. Sternberg in the November 1973 Scientific American.) This flea was about 2 mm long and jumped at a nearly vertical takeoff angle. Use the graph to answer these questions: (a) Is the acceleration of the flea ever zero? If so, when? Justify your answer.

Verified Solution
Video duration:
2m
This video solution was recommended by our tutors as helpful for the problem above.
658
views
Was this helpful?

Video transcript

Hey everyone welcome back in this problem. We're using high speed motion pictures to analyze projectile launch from a toy gun. Okay. We're told it's launched at near vertical angle It's 20 g and five cm long. And we get the graph below generated by using the motion pictures And from the graph we want to find when is the acceleration of the projectile zero. Alright, so we're asked about acceleration and let's see here our graph, we have velocity versus time. Yes, we have a velocity time graph. Okay. And so when we're thinking about the relationship between acceleration and a V. T graph, we know that the acceleration okay, is going to be equal to the slope of the curve on our V. T. Graph. Alright, so we're looking for an acceleration of zero. We know that on our on our graph the acceleration is the slope of the curve. Okay, if we want acceleration equals to zero, this means that we want a slope Equal to zero on our graph. Okay, well a slope Equals to zero means that we have a horizontal wine. So let's look at our graph. Where do we see a horizontal line? We see a horizontal line here. Okay, where the slope is zero. So our acceleration is zero. And if we draw down to see what time that is at, we see that this starts at 100 and 50 milliseconds. Okay, so starting at T equals 100 and 50 milliseconds and going onward we are going to have a horizontal line which means the slope of zero, which means an acceleration of zero. Okay, So we're gonna go with Answer B when T is bigger or equal to 150 milliseconds. Alright, that's it for this problem. I hope this video helped see you in the next one.
Previous problemNext problem
Related Practice
Textbook Question
A cat walks in a straight line, which we shall call the x-axis, with the positive direction to the right. As an observant physicist, you make measurements of this cat's motion and construct a graph of the feline's velocity as a function of time (Fig. E2.30). (c) What distance does the cat move during the first 4.5 s? From t = 0 to t = 7.5 s?

816
views
Textbook Question
A cat walks in a straight line, which we shall call the x-axis, with the positive direction to the right. As an observant physicist, you make measurements of this cat's motion and construct a graph of the feline's velocity as a function of time (Fig. E2.30). (d) Assuming that the cat started at the origin, sketch clear graphs of the cat's acceleration and position as functions of time.

1356
views
Textbook Question
The Fastest (and Most Expensive) Car! The table shows test data for the Bugatti Veyron Super Sport, the fastest street car made. The car is moving in a straight line (the x-axis). (a) Sketch a vx–t graph of this car's velocity (in mi/h) as a function of time. Is its acceleration constant? (b) Calculate the car's average acceleration (in m/s2) between (i) 0 and 2.1 s; (ii) 2.1 s and 20.0 s; (iii) 20.0 s and 53 s. Are these results consistent with your graph in part (a)? (Before you decide to buy this car, it might be helpful to know that only 300 will be built, it runs out of gas in 12 minutes at top speed, and it costs more than $1.5 million!)

753
views
Textbook Question
High-speed motion pictures (3500 frames/second) of a jumping, 210–μg flea yielded the data used to plot the graph in Fig. E2.54. (See 'The Flying Leap of the Flea' by M. Rothschild, Y. Schlein, K. Parker, C. Neville, and S. Sternberg in the November 1973 Scientific American.) This flea was about 2 mm long and jumped at a nearly vertical takeoff angle. Use the graph to answer these questions: (b) Find the maximum height the flea reached in the first 2.5 ms.

717
views
Textbook Question
High-speed motion pictures (3500 frames/second) of a jumping, 210–μg flea yielded the data used to plot the graph in Fig. E2.54. (See 'The Flying Leap of the Flea' by M. Rothschild, Y. Schlein, K. Parker, C. Neville, and S. Sternberg in the November 1973 Scientific American.) This flea was about 2 mm long and jumped at a nearly vertical takeoff angle. Use the graph to answer these questions: (c) Find the flea's acceleration at 0.5 ms, 1.0 ms, and 1.5 ms.

569
views
Textbook Question
A brick is dropped (zero initial speed) from the roof of a building. The brick strikes the ground in 1.90 s. You may ignore air resistance, so the brick is in free fall. (a) How tall, in meters, is the building?
565
views