Courses
Courses for Kids
Free study material
Offline Centres
More
Store

# QuestionIn Exercises 2.9 and 2.10, we have carefully distinguished between average speed and magnitude of average velocity. No such distinction is necessary when we consider instantaneous speed and magnitude of velocity. The instantaneous speed is always equal to the magnitude of instantaneous velocity. Why?

Last updated date: 21st Jun 2024
Total views: 64.5k
Views today: 0.64k
Verified
64.5k+ views

Solution:
Hint

The instantaneous speed is the rate of change of the particle's position with respect to time. The instantaneous velocity is the vector representation of the instantaneous speed, which means that it includes both the magnitude and direction of the motion.

Step-by-step Solution:

1. Consider the definition of instantaneous speed and instantaneous velocity.

• Instantaneous speed: The rate of change of the particle's position with respect to time.

• Instantaneous velocity: The vector representation of the instantaneous speed, which means that it includes both the magnitude and direction of the motion.

1. Recognize that for infinitesimally small time intervals, the motion of the particle can be approximated to be uniform.

• This means that the particle will not have enough time to change its direction significantly during this time interval.

1. Therefore, the instantaneous velocity and instantaneous speed will have the same magnitude and direction.