State whether the following statements are true or false:
$(a)$ If the motion is not along a straight line,then path length = magnitude of displacement.
$(b)$ Stopping distance is directly proportional to the initial velocity.
$(c)$ The average speed of an object moving with different speeds is the average of those speeds.
$(d)$ The area under the position-time graph represents the displacement of the moving object.
$(a)$ If the motion is not along a straight line,then path length = magnitude of displacement.
$(b)$ Stopping distance is directly proportional to the initial velocity.
$(c)$ The average speed of an object moving with different speeds is the average of those speeds.
$(d)$ The area under the position-time graph represents the displacement of the moving object.
(NONE) False. For non-linear motion,path length is always greater than the magnitude of displacement.
$(b)$ False. Stopping distance $d_s = \frac{v^2}{2a}$,so it is proportional to the square of the initial velocity.
$(c)$ False. Average speed is defined as the total distance traveled divided by the total time taken,not the arithmetic mean of individual speeds.
$(d)$ False. The slope of the position-time graph represents velocity. The area under a velocity-time graph represents displacement.
$(b)$ False. Stopping distance $d_s = \frac{v^2}{2a}$,so it is proportional to the square of the initial velocity.
$(c)$ False. Average speed is defined as the total distance traveled divided by the total time taken,not the arithmetic mean of individual speeds.
$(d)$ False. The slope of the position-time graph represents velocity. The area under a velocity-time graph represents displacement.
Explore More
Similar Questions
Match the following columns.
Column $I$ Column $II$ $(A)$ Constant positive acceleration $(p)$ Speed may increase $(B)$ Constant negative acceleration $(q)$ Speed may decrease $(C)$ Constant displacement $(r)$ Speed is zero $(D)$ Constant slope of $a-t$ graph $(s)$ Speed must increase
| Column $I$ | Column $II$ |
| $(A)$ Constant positive acceleration | $(p)$ Speed may increase |
| $(B)$ Constant negative acceleration | $(q)$ Speed may decrease |
| $(C)$ Constant displacement | $(r)$ Speed is zero |
| $(D)$ Constant slope of $a-t$ graph | $(s)$ Speed must increase |
Medium
View Solution$A$ street car moves rectilinearly from station $A$ to the next station $B$ with an acceleration varying according to the law $a = (b - cx)$,where $b$ and $c$ are constants and $x$ is the distance from station $A$. The distance between the two stations and the maximum velocity are:
Difficult
View SolutionThe displacement $x$ of a particle depends on time $t$ as $x = \alpha t^2 - \beta t^3$.
Difficult
View SolutionSelect the incorrect statement among the following$:-$
$S_1 :$ If the acceleration is zero,a moving particle will perform uniform motion.
$S_2 :$ Motion with constant speed may or may not be uniform motion.
$S_3 :$ If a particle moves on a curved path,its acceleration can never be zero.
$S_4 :$ In successive time intervals,if the average velocities of a particle are equal,then the particle must be moving with uniform velocity.
$S_1 :$ If the acceleration is zero,a moving particle will perform uniform motion.
$S_2 :$ Motion with constant speed may or may not be uniform motion.
$S_3 :$ If a particle moves on a curved path,its acceleration can never be zero.
$S_4 :$ In successive time intervals,if the average velocities of a particle are equal,then the particle must be moving with uniform velocity.
Medium
View SolutionFor a particle showing motion under the force $F = -5(x - 2)^2$,the motion is .......
Easy
View SolutionVedclass Products
For Students
Vedclass Test Series
Mock tests in real JEE/NEET style with performance analysis. 5-day free trial.
Start Free TrialFor Teachers
Exam Paper Generator
Generate Set A/B/C/D exam papers from 7.5L+ questions in 2 minutes. 3 chapters free.
Try FreeFor Institutes
Online Exam Module
Live online exams with unlimited students, 360° analytics & white-label branding.
See Demo