Class 11 Exam  >  Class 11 Questions  >  The position-time graphs of two cars A and B ... Start Learning for Free
The position-time graphs of two cars A and B are straight lines making 30 degreeand 60degree with the time axis respectively. The ratio of velocities of A and B is?
Verified Answer
The position-time graphs of two cars A and B are straight lines making...
Slope of position time graph gives velocity i.e v=dx/dt=tan theta va/vb=tan 30/tan 60=1/3
This question is part of UPSC exam. View all Class 11 courses
Most Upvoted Answer
The position-time graphs of two cars A and B are straight lines making...
Position-time graphs of cars A and B

Car A and Car B have position-time graphs that are straight lines making angles of 30 degrees and 60 degrees with the time axis, respectively. In order to find the ratio of velocities of A and B, we need to analyze the slopes of their position-time graphs.

Slope of the position-time graph

The slope of a position-time graph represents the velocity of an object. It is the rate at which the position of the object changes with respect to time. Mathematically, the slope can be calculated as the change in position divided by the change in time.

Calculating the slope of the position-time graph for Car A

The angle made by the position-time graph of Car A with the time axis is 30 degrees. Let's assume the slope of Car A's graph is m1.

tan(30 degrees) = m1
1/sqrt(3) = m1

Therefore, the slope of Car A's position-time graph is 1/sqrt(3).

Calculating the slope of the position-time graph for Car B

The angle made by the position-time graph of Car B with the time axis is 60 degrees. Let's assume the slope of Car B's graph is m2.

tan(60 degrees) = m2
sqrt(3) = m2

Therefore, the slope of Car B's position-time graph is sqrt(3).

Ratio of velocities of A and B

The ratio of velocities of Car A and Car B can be calculated by dividing their respective slopes.

Velocity of Car A / Velocity of Car B = m1 / m2
Velocity of Car A / Velocity of Car B = (1/sqrt(3)) / sqrt(3)
Velocity of Car A / Velocity of Car B = 1/3

Therefore, the ratio of velocities of Car A and Car B is 1:3.

Explanation

The ratio of velocities of Car A and Car B is determined by the slopes of their position-time graphs. The slopes represent the rates at which their positions change with respect to time. By calculating the slopes using the angles made by their graphs with the time axis, we can determine the ratio of their velocities. In this case, the ratio is 1:3, indicating that Car B is three times faster than Car A.
Attention Class 11 Students!
To make sure you are not studying endlessly, EduRev has designed Class 11 study material, with Structured Courses, Videos, & Test Series. Plus get personalized analysis, doubt solving and improvement plans to achieve a great score in Class 11.
Explore Courses for Class 11 exam

Top Courses for Class 11

The position-time graphs of two cars A and B are straight lines making 30 degreeand 60degree with the time axis respectively. The ratio of velocities of A and B is?
Question Description
The position-time graphs of two cars A and B are straight lines making 30 degreeand 60degree with the time axis respectively. The ratio of velocities of A and B is? for Class 11 2024 is part of Class 11 preparation. The Question and answers have been prepared according to the Class 11 exam syllabus. Information about The position-time graphs of two cars A and B are straight lines making 30 degreeand 60degree with the time axis respectively. The ratio of velocities of A and B is? covers all topics & solutions for Class 11 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for The position-time graphs of two cars A and B are straight lines making 30 degreeand 60degree with the time axis respectively. The ratio of velocities of A and B is?.
Solutions for The position-time graphs of two cars A and B are straight lines making 30 degreeand 60degree with the time axis respectively. The ratio of velocities of A and B is? in English & in Hindi are available as part of our courses for Class 11. Download more important topics, notes, lectures and mock test series for Class 11 Exam by signing up for free.
Here you can find the meaning of The position-time graphs of two cars A and B are straight lines making 30 degreeand 60degree with the time axis respectively. The ratio of velocities of A and B is? defined & explained in the simplest way possible. Besides giving the explanation of The position-time graphs of two cars A and B are straight lines making 30 degreeand 60degree with the time axis respectively. The ratio of velocities of A and B is?, a detailed solution for The position-time graphs of two cars A and B are straight lines making 30 degreeand 60degree with the time axis respectively. The ratio of velocities of A and B is? has been provided alongside types of The position-time graphs of two cars A and B are straight lines making 30 degreeand 60degree with the time axis respectively. The ratio of velocities of A and B is? theory, EduRev gives you an ample number of questions to practice The position-time graphs of two cars A and B are straight lines making 30 degreeand 60degree with the time axis respectively. The ratio of velocities of A and B is? tests, examples and also practice Class 11 tests.
Explore Courses for Class 11 exam

Top Courses for Class 11

Explore Courses
Signup for Free!
Signup to see your scores go up within 7 days! Learn & Practice with 1000+ FREE Notes, Videos & Tests.
10M+ students study on EduRev