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Chapter 2: Problem 182

The ratio of pathlength and the respective time interval is (A) Mean Velocity (B) Mean speed (C) instantaneous velocity (D) instantaneous speed

Short Answer

Expert verified
The given ratio \(\frac{\text{pathlength}}{\text{time interval}}\) represents (B) Mean speed, as it closely resembles the definition of mean speed, which involves the total distance (pathlength) divided by the time interval, without considering the direction of motion.

Step by step solution

01

Understand the given ratio

The question gives us a ratio: \(\frac{\text{pathlength}}{\text{time interval}}\). We need to find out which of the given concepts this represents.
02

Define mean velocity

Mean velocity is the total displacement divided by the total time interval. Displacement is the change in position and takes into account the direction of the movement.
03

Define mean speed

Mean speed is the total distance covered divided by the total time interval. Distance is the length of the path taken during the motion, and it doesn't consider the direction.
04

Define instantaneous velocity

Instantaneous velocity is the velocity of an object at a specific instant in time. It tells us how fast an object is moving while considering its direction.
05

Define instantaneous speed

Instantaneous speed is the magnitude of the instantaneous velocity, which means it only tells us how fast an object is moving but does not consider the direction.
06

Compare the given ratio to the definitions

In the given ratio, \(\frac{\text{pathlength}}{\text{time interval}}\), pathlength refers to the distance covered, and it doesn't consider the direction of the object. So, it can't be mean velocity or instantaneous velocity because both require considering the direction of motion (displacement). However, when we compare the ratio to the definitions of mean speed and instantaneous speed, we see that the given ratio closely resembles the definition of mean speed, as both involve the total distance (pathlength) divided by the time interval.
07

Determine the correct option

Based on our comparison, the ratio of pathlength and the respective time interval represents (B) Mean speed.

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Most popular questions from this chapter

$ \mathrm{A}^{\rightarrow}=3 \hat{\imath}+2 \hat{\jmath}-5 \mathrm{k}^{\wedge}\( and \)\mathrm{B}^{\rightarrow}=\hat{\imath}+\hat{\jmath}+2 \mathrm{k}^{\wedge}\( Find \)\left|\mathrm{A}^{\rightarrow}+2 \mathrm{~B}^{\rightarrow}\right|$ (A) \(\sqrt{40}\) (B) \(\sqrt{42}\) (C) \(\sqrt{39}\) (D) 2

A particle is projected vertically upwards with velocity $30 \mathrm{~ms}^{-1}$. Find the ratio of average speed and instantaneous velocity after 6 s. \(\left[\mathrm{g}=10 \mathrm{~ms}^{-1}\right]\) (A) \((1 / 2)\) (B) 2 (C) 3 (D) 4

If $\mathrm{A}^{\rightarrow}=2 \mathrm{i} \wedge+5 \mathrm{j} \wedge-\mathrm{k} \wedge\( and \)\mathrm{B}^{\rightarrow}=3 \mathrm{i} \wedge-2 \mathrm{j} \wedge-4 \mathrm{k} \wedge$ the angle between \(\mathrm{A}^{\rightarrow}\) and \(\mathrm{B}^{\rightarrow}\) is (A) 0 (B) \((\pi / 2)\) (C) \((\pi / 4)\) (D) \((\pi / 6)\)

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A particle has initial velocity \((2 \hat{1}+3 \hat{j}) \mathrm{ms}^{-1}\) and has acceleration \((\hat{1}+\hat{j}) \mathrm{ms}^{-2}\). Find the velocity of the particle after 2 second. (A) \((3 \hat{1}+5 \hat{j}) \mathrm{ms}^{-1}\) (B) \((4 \hat{i}+5 \hat{\jmath}) \mathrm{ms}^{-1}\) (C) \((3 \hat{1}+2 \hat{j}) \mathrm{ms}^{-1}\) (D) \((5 \hat{1}+4 \hat{j}) \mathrm{ms}^{-1}\)
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