Log out Go to App
Go to App

Learning Materials

Features

Discover

Chapter 2: Q. 9 (page 59)

FIGURE EX2.9 shows the velocity graph of a particle. Draw the particle’s acceleration graph for the interval 0s≤t≤4s

Short Answer

Expert verified

The graph of the acceleration of the particle is shown below

Step by step solution

01

Acceleration of a particle.

Acceleration is the slope of the velocity-time graph.

Consider two points on the graph, t1,v1=0,2and t2,v2=2,2.

The slope of the velocity-time graph is

ax=v2-v1t2-t1=2-22-0=0ms2

Now consider points t2,v2=2,2and t3,v3=4,4.

The slope of the velocity-time graph is

ax=v3-v2t3-t2=4-24-2=22=1ms2

02

Graph of particle’s acceleration.

From the information obtained in step 1, draw a graph of the acceleration of the particle.

The graph of the acceleration of the particle is shown below.

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

Careful measurements have been made of Olympic sprinters in the 100-meter dash. A simple but reasonably accurate model is that a sprinter accelerates at 3.6 m/s2 for 31 3 s, then runs at constant velocity to the finish line.
a. What is the race time for a sprinter who follows this model?
b. A sprinter could run a faster race by accelerating faster at the beginning, thus reaching top speed sooner. If a sprinter’s top speed is the same as in part a, what acceleration would he need to run the 100-meter dash in 9.9 s?
c. By what percent did the sprinter need to increase his acceleration in order to decrease his time by 1%?

FIGURE EX2.31 shows the acceleration-versus-time graph of a particle moving along the x-axis. Its initial velocity is v0x = 8.0 m/s at t0 = 0 s. What is the particle’s velocity at t = 4.0 s?

Careful measurements have been made of Olympic sprinters

in the 100 meter dash. A quite realistic model is that the sprinter’s

velocity is given by

vx=a(1-e-bt)

where t is in s, vx is in m/s, and the constants a and b are characteristic

of the sprinter. Sprinter Carl Lewis’s run at the 1987

World Championships is modeled with a = 11.81 m/s and

b = 0.6887 s-1.

a. What was Lewis’s acceleration at t = 0 s, 2.00 s, and 4.00 s?

b. Find an expression for the distance traveled at time t.

c. Your expression from part b is a transcendental equation,

meaning that you can’t solve it for t. However, it’s not hard to

use trial and error to find the time needed to travel a specific

distance. To the nearest 0.01 s, find the time Lewis needed to

sprint 100.0 m. His official time was 0.01 s more than your

answer, showing that this model is very good, but not perfect.

Careful measurements have been made of Olympic sprinters in the 100 meter dash. A simple but reasonably accurate model is that a sprinter accelerates at 3.6 m/s2 for 313s, then runs at constant velocity to the finish line.

a. What is the race time for a sprinter who follows this model?

b. A sprinter could run a faster race by accelerating faster at the beginning, thus reaching top speed sooner. If a sprinter’s top speed is the same as in part a, what acceleration would he need to run the 100 meter dash in 9.9 s?

c. By what percent did the sprinter need to increase his acceleration in order to decrease his time by 1%?

A rubber ball is shot straight up from the ground with speed v0. Simultaneously, a second rubber ball at a height h directly above the first ball is dropped from rest.
a. At what height above the ground do the balls collide? Your answer will be an algebraic expression in terms of h, v0, and g.
b. What is the maximum value of h for which a collision occurs before the first ball falls back to the ground?
c. For what value of h does the collision occur at the instant when the first ball is at its highest point?
See all solutions

Recommended explanations on Physics Textbooks

Scientific Method Physics

Read Explanation

Turning Points in Physics

Read Explanation

Magnetism

Read Explanation

Medical Physics

Read Explanation

Electricity

Read Explanation

Electromagnetism

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