What is a velocity-time graph? State how it can be used to find:
$(i)$ The acceleration of a body.
$(ii)$ The displacement of the body.
$(iii)$ The distance travelled in a given time.
$(i)$ The acceleration of a body.
$(ii)$ The displacement of the body.
$(iii)$ The distance travelled in a given time.
(N/A) In a velocity-time graph,time is plotted along the $x$-axis and velocity is plotted along the $y$-axis.
$(i)$ Since acceleration $=$ Change in velocity $/$ Time,the slope of the velocity-time graph gives the acceleration. If the slope is positive,it represents accelerated motion; if the slope is negative,it represents retarded motion.
$(ii)$ Since velocity $\times$ time $=$ displacement,the area enclosed between the graph and the time axis represents the displacement. The area above the time axis is considered positive displacement,and the area below the time axis is considered negative displacement. The total displacement is the algebraic sum of these areas.
$(iii)$ The total distance travelled by the body is the arithmetic sum of the magnitudes of the areas enclosed by the velocity-time graph and the time axis (ignoring the sign).
$(i)$ Since acceleration $=$ Change in velocity $/$ Time,the slope of the velocity-time graph gives the acceleration. If the slope is positive,it represents accelerated motion; if the slope is negative,it represents retarded motion.
$(ii)$ Since velocity $\times$ time $=$ displacement,the area enclosed between the graph and the time axis represents the displacement. The area above the time axis is considered positive displacement,and the area below the time axis is considered negative displacement. The total displacement is the algebraic sum of these areas.
$(iii)$ The total distance travelled by the body is the arithmetic sum of the magnitudes of the areas enclosed by the velocity-time graph and the time axis (ignoring the sign).
Explore More
Similar Questions
Starting from rest at the top of an inclined plane, a body reaches the bottom of the inclined plane in $4$ seconds. In what time does the body cover one-fourth of the distance starting from rest at the top?
Difficult
View Solution"The direction in which an object moves is given by the direction of velocity of the object and not by the direction of acceleration." Give an example to justify this statement.
Easy
View Solution$A$ car travels $100\, km$ east and then $100\, km$ south. Finally,it comes back to the starting point by the south-east route. Throughout the journey the speed is constant at $60\, km\, h^{-1}$. The average velocity for the whole journey if the time taken is $3.3\, h$ is
Medium
View SolutionWhat is the slope of the displacement $-$ time graph when the body has uniform motion?
Easy
View Solution$A$ body moves with a velocity of $2\, m s^{-1}$ for $5\, s$,then its velocity increases uniformly to $10\, m s^{-1}$ in the next $5\, s$. Thereafter,its velocity begins to decrease at a uniform rate until it comes to rest after $5\, s$.
$(i)$ Plot a velocity-time graph for the motion of the body.
$(ii)$ From the graph,find the total distance covered by the body after $2\, s$ and $12\, s$.
$(i)$ Plot a velocity-time graph for the motion of the body.
$(ii)$ From the graph,find the total distance covered by the body after $2\, s$ and $12\, s$.
Medium
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