Log out Go to App
Go to App

Learning Materials

Features

Discover

Chapter 3: Problem 30

A runner times his speed around a track with a circumference of $0.50 \mathrm{mi} .\( He finds that he has run a distance of \)1.00 \mathrm{mi}$ in 4.0 min. What is his (a) average speed and (b) average velocity magnitude in \(\mathrm{m} / \mathrm{s}\) ?

Short Answer

Expert verified
Answer: The runner's (a) average speed is 6.71 m/s, and (b) his average velocity magnitude is 0 m/s.

Step by step solution

01

Convert given units to meters and seconds

We need to convert the given distances from miles to meters and the time from minutes to seconds. We do that by multiplying by the conversion factor. 1 mile = 1609.34 meters 1 minute = 60 seconds Circumference = 0.50 mi * 1609.34 m/mi = 804.67 m Distance traveled = 1.00 mi * 1609.34 m/mi = 1609.34 m Time taken = 4.0 min * 60 s/min = 240 s Now we have all distances in meters and times in seconds.
02

Calculate average speed

Average speed is calculated by dividing the distance run by the time taken. We have the distance traveled (1609.34 m) and the time taken (240 s): Average_speed = (Distance_traveled) / (Time_taken) Average_speed = 1609.34 m / 240 s ≈ 6.71 m/s The runner's average speed is approximately 6.71 m/s.
03

Calculate the total displacement

Displacement means the change in position from the starting point. Since the runner is moving in a circular track, after covering the 1-mile distance, he has done 2 full laps around the track (1 mile / 0.5-mile circumference). Returning to the starting point after each lap, the total displacement becomes 0. Total_displacement = 0 m
04

Calculate the average velocity magnitude

Since the total displacement is 0, the average velocity magnitude is also 0: Average_velocity_magnitude = (Total_displacement) / (Time_taken) Average_velocity_magnitude = 0 m / 240 s = 0 m/s The runner's average velocity magnitude is 0 m/s. In conclusion, the runner's (a) average speed is 6.71 m/s, and (b) his average velocity magnitude is 0 m/s.

Unlock Step-by-Step Solutions & Ace Your Exams!

  • Full Textbook Solutions

    Get detailed explanations and key concepts

  • Unlimited Al creation

    Al flashcards, explanations, exams and more...

  • Ads-free access

    To over 500 millions flashcards

  • Money-back guarantee

    We refund you if you fail your exam.

Start your free trial

Over 30 million students worldwide already upgrade their learning with Vaia!

One App. One Place for Learning.

All the tools & learning materials you need for study success - in one app.

Get started for free

Most popular questions from this chapter

A marble is rolled so that it is projected horizontally off the top landing of a staircase. The initial speed of the marble is $3.0 \mathrm{m} / \mathrm{s} .\( Each step is \)0.18 \mathrm{m}\( high and \)0.30 \mathrm{m}$ wide. Which step does the marble strike first?
Vector \(\overrightarrow{\mathbf{B}}\) has magnitude 7.1 and direction \(14^{\circ}\) below the \(+x\) -axis. Vector \(\quad \overrightarrow{\mathbf{C}}\) has \(x\) -component \(C_{x}=-1.8\) and \(y\) -component \(C_{y}=-6.7 .\) Compute \((a)\) the \(x-\) and \(y\) -components of \(\overrightarrow{\mathbf{B}} ;\) (b) the magnitude and direction of \(\overrightarrow{\mathbf{C}} ;\) (c) the magnitude and direction of \(\overrightarrow{\mathbf{C}}+\overrightarrow{\mathbf{B}} ;\) (d) the magnitude and direction of \(\overrightarrow{\mathbf{C}}-\overrightarrow{\mathbf{B}} ;\) (e) the \(x\) - and \(y\) -components of \(\overrightarrow{\mathbf{C}}-\overrightarrow{\mathbf{B}}\)
Michaela is planning a trip in Ireland from Killarney to Cork to visit Blarney Castle. (See Example \(3.2 .\) ) She also wants to visit Mallow, which is located \(39 \mathrm{km}\) due east of Killarney and \(22 \mathrm{km}\) due north of Cork. Draw the displacement vectors for the trip when she travels from Killarney to Mallow to Cork. (a) What is the magnitude of her displacement once she reaches Cork? (b) How much additional distance does Michaela travel in going to Cork by way of Mallow instead of going directly from Killarney to Cork?
You have been employed by the local circus to plan their human cannonball performance. For this act, a spring-loaded cannon will shoot a human projectile, the Great Flyinski, across the big top to a net below. The net is located \(5.0 \mathrm{m}\) lower than the muzzle of the cannon from which the Great Flyinski is launched. The cannon will shoot the Great Flyinski at an angle of \(35.0^{\circ}\) above the horizontal and at a speed of $18.0 \mathrm{m} / \mathrm{s} .$ The ringmaster has asked that you decide how far from the cannon to place the net so that the Great Flyinski will land in the net and not be splattered on the floor, which would greatly disturb the audience. What do you tell the ringmaster? ( Wheractive: projectile motion)
John drives \(16 \mathrm{km}\) directly west from Orion to Chester at a speed of \(90 \mathrm{km} / \mathrm{h},\) then directly south for \(8.0 \mathrm{km}\) to Seiling at a speed of \(80 \mathrm{km} / \mathrm{h}\), then finally $34 \mathrm{km}\( southeast to Oakwood at a speed of \)100 \mathrm{km} / \mathrm{h}$. Assume he travels at constant velocity during each of the three segments. (a) What was the change in velocity during this trip? [Hint: Do not assume he starts from rest and stops at the end.] (b) What was the average acceleration during this trip?
See all solutions

Recommended explanations on Physics Textbooks

Geometrical and Physical Optics

Read Explanation

Astrophysics

Read Explanation

Circular Motion and Gravitation

Read Explanation

Torque and Rotational Motion

Read Explanation

Electrostatics

Read Explanation

Physical Quantities And Units

Read Explanation
View all explanations

What do you think about this solution?

We value your feedback to improve our textbook solutions.

Study anywhere. Anytime. Across all devices.

Sign-up for free