Answer The correct answer is (a) at time, t = 2 sec , 7 sec body moves in reverse direction. (b) At time, t = 3 sec to 6 sec body moves in constant direction. (c) See the graph in explanation part. (d) See the graph in explanation part. Explanation Given information: The velocity-time graph of a body is given, and through this graph we have to find the time when body moves in reverse direction, find the time when the body moving at constant speed. Draw the graph body’s speed for 0 ≤ t < 10 .Draw the graph acceleration, where defined. Calculation: We know that, the condition to move body in reverse direction is when the velocity of the body becomes zero. See the graph carefully at time t = 2 sec and t = 7 sec velocity is zero. Hence we can say at time, t = 2 sec , 7 sec body moves in reverse direction. We know that, the condition to move body at constant velocity is when the magnitude of velocity will not change during the given time or in different we can say acceleration value becomes zero. See the graph carefully, during the time t = 3 sec to 6 sec body moves in constant speed (absolute value of velocity). We know that, Speed is a scalar quantity, hence there is no direction, but in velocity some direction are there, to draw the graph of speed-time we have to take absolute value of velocity-time graph. Speed v/s Time graph We know that a = d v d t , to find acceleration graph we will differentiate velocity-time graph, and we also know that differentiation of line is constant function, and differentiation of constant function is zero. See the graph carefully, Acceleration v/s Time graph

Calculus 2012 Student Edition (by Finney/Demana/Waits/Kennedy)

4th Edition

ISBN: 9780133178579

Author: Ross L. Finney

Publisher: PEARSON

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Question

Chapter 3.4, Problem 11E

To determine

To calculate: Find (a) the time when body moves in reverse direction.

(b) The time when the body moving at constant speed.

(c) The graph body’s speed for 0≤t<10.

(d) The graph acceleration, where defined.

Expert Solution & Answer

Answer to Problem 11E

The correct answer is (a) at time, t=2sec,7sec body moves in reverse direction.

(b) At time, t=3sec to 6sec body moves in constant direction.

(d) See the graph in explanation part.

Explanation of Solution

Given information: The velocity-time graph of a body is given, and through this graph we have to find the time when body moves in reverse direction, find the time when the body moving at constant speed. Draw the graph body’s speed for 0≤t<10 .Draw the graph acceleration, where defined.

Calculation:

We know that, the condition to move body in reverse direction is when the velocity of the body becomes zero. See the graph carefully at time t=2sec and t=7sec velocity is zero. Hence we can say at time, t=2sec,7sec body moves in reverse direction.
We know that, the condition to move body at constant velocity is when the magnitude of velocity will not change during the given time or in different we can say acceleration value becomes zero. See the graph carefully, during the time t=3sec to 6sec body moves in constant speed (absolute value of velocity).
We know that, Speed is a scalar quantity, hence there is no direction, but in velocity some direction are there, to draw the graph of speed-time we have to take absolute value of velocity-time graph.

Calculus 2012 Student Edition (by Finney/Demana/Waits/Kennedy), Chapter 3.4, Problem 11E , additional homework tip 1

Speed v/s Time graph

We know that a=dvdt, to find acceleration graph we will differentiate velocity-time graph, and we also know that differentiation of line is constant function, and differentiation of constant function is zero. See the graph carefully,

Calculus 2012 Student Edition (by Finney/Demana/Waits/Kennedy), Chapter 3.4, Problem 11E , additional homework tip 2

Acceleration v/s Time graph

Chapter 3.4, Problem 10E

Chapter 3.4, Problem 12E

Chapter 3 Solutions

Calculus 2012 Student Edition (by Finney/Demana/Waits/Kennedy)

Ch. 3.1 - Prob. 1QR Ch. 3.1 - Prob. 2QR Ch. 3.1 - Prob. 3QR Ch. 3.1 - Prob. 4QR Ch. 3.1 - Prob. 5QR Ch. 3.1 - Prob. 6QR Ch. 3.1 - Prob. 7QR Ch. 3.1 - Prob. 8QR Ch. 3.1 - Prob. 9QR Ch. 3.1 - Prob. 10QR

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