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Chapter 2: Problem 64

In the problems, please assume the free-fall acceleration $g=9.80 \mathrm{m} / \mathrm{s}^{2}$ unless a more precise value is given in the problem statement. Ignore air resistance. To pass a physical fitness test, Marcella must run \(1000 \mathrm{m}\) at an average speed of \(4.00 \mathrm{m} / \mathrm{s} .\) She runs the first $500 \mathrm{m}\( at an average of \)4.20 \mathrm{m} / \mathrm{s} .$ (a) How much time does she have to run the last \(500 \mathrm{m} ?\) (b) What should be her average speed over the last \(500 \mathrm{m}\) in order to finish with an overall average speed of \(4.00 \mathrm{m} / \mathrm{s} ?\)

Short Answer

Expert verified
Answer: (a) Marcella has 130.95 seconds to run the last 500 meters, and (b) she should have an average speed of approximately 3.82 m/s for the last 500 meters to achieve the desired overall average speed.

Step by step solution

01

Calculate the time taken for the first 500m

We are given that Marcella runs the first 500m at an average speed of 4.20 m/s. We will use the formula for average speed to find the time taken for the first 500m. Average speed = Distance / Time 4.20 m/s = 500m / Time Time = 500m / 4.20 m/s = 119.05 s
02

Calculate the total time for 1000m

Since Marcella needs to run the full 1000m at an average speed of 4.00 m/s, we can find the total time for the run using the same formula: 4.00 m/s = 1000m /Total Time Total Time = 1000m / 4.00 m/s = 250.00 s
03

Calculate the time allowed for the last 500m

Now that we know the total time and the time taken for the first 500m, we can find the time allowed for the last 500m: Time allowed for the last 500m = Total Time - Time taken for the first 500m Time allowed for the last 500m = 250.00 s - 119.05 s = 130.95 s
04

Calculate the required average speed for the last 500m

To find the required average speed for the last 500m, we will use the formula for average speed: Required average speed = Distance / Time Required average speed = 500m / 130.95 s ≈ 3.82 m/s So, the answers are: (a) Marcella has 130.95 seconds to run the last 500 meters, and (b) She should have an average speed of approximately 3.82 m/s during the last 500 meters to finish the race with the desired overall average speed of 4.00 m/s.

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Most popular questions from this chapter

In the human nervous system, signals are transmitted along neurons as action potentials that travel at speeds of up to \(100 \mathrm{m} / \mathrm{s} .\) (An action potential is a traveling influx of sodium ions through the membrane of a neuron.) The signal is passed from one neuron to another by the release of neurotransmitters in the synapse. Suppose someone steps on your toe. The pain signal travels along a 1.0 -m-long sensory neuron to the spinal column, across a synapse to a second 1.0 -m-long neuron, and across a second synapse to the brain. Suppose that the synapses are each \(100 \mathrm{nm}\) wide, that it takes \(0.10 \mathrm{ms}\) for the signal to cross each synapse, and that the action potentials travel at \(100 \mathrm{m} / \mathrm{s} .\) (a) At what average speed does the signal cross a synapse? (b) How long does it take the signal to reach the brain? (c) What is the average speed of propagation of the signal?
A 1200 -kg airplane starts from rest and moves forward with a constant acceleration of magnitude \(5.00 \mathrm{m} / \mathrm{s}^{2}\) along a runway that is 250 m long. (a) How long does it take the plane to reach a speed of \(46.0 \mathrm{m} / \mathrm{s} ?\) (b) How far along the runway has the plane moved when it reaches \(46.0 \mathrm{m} / \mathrm{s} ?\)
please assume the free-fall acceleration \(g=9.80 \mathrm{m} / \mathrm{s}^{2}\) unless a more precise value is given in the problem statement. Ignore air resistance. During a walk on the Moon, an astronaut accidentally drops his camera over a 20.0 -m cliff. It leaves his hands with zero speed, and after \(2.0 \mathrm{s}\) it has attained a velocity of \(3.3 \mathrm{m} / \mathrm{s}\) downward. How far has the camera fallen after \(4.0 \mathrm{s} ?\)
A ball thrown by a pitcher on a women's softball team is timed at 65.0 mph. The distance from the pitching rubber to home plate is \(43.0 \mathrm{ft}\). In major league baseball the corresponding distance is \(60.5 \mathrm{ft}\). If the batter in the softball game and the batter in the baseball game are to have equal times to react to the pitch, with what speed must the baseball be thrown? Assume the ball travels with a constant velocity. [Hint: There is no need to convert units; set up a ratio.]
The St. Charles streetcar in New Orleans starts from rest and has a constant acceleration of \(1.20 \mathrm{m} / \mathrm{s}^{2}\) for \(12.0 \mathrm{s} .\) (a) Draw a graph of \(v_{x}\) versus \(t .\) (b) How far has the train traveled at the end of the \(12.0 \mathrm{s} ?\) (c) What is the speed of the train at the end of the \(12.0 \mathrm{s} ?\) (d) Draw a motion diagram, showing the streetcar's position at \(2.0-\mathrm{s}\) intervals.
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