$(a)$ Derive graphically the equation for velocity$-$time relation.
$(b)$ Name the device used to measure distance travelled by a vehicle.
$(c)$ Can displacement of a moving object be zero? Give reason.
$(b)$ Name the device used to measure distance travelled by a vehicle.
$(c)$ Can displacement of a moving object be zero? Give reason.
(N/A) Consider a velocity$-$time graph where an object starts with initial velocity $u$ at time $t=0$ and reaches final velocity $v$ at time $t$. The slope of the velocity$-$time graph represents acceleration $(a)$.
Slope $= \frac{\text{Change in velocity}}{\text{Time taken}} = \frac{v - u}{t}$.
Therefore,$a = \frac{v - u}{t}$,which gives $at = v - u$,or $v = u + at$.
$(b)$ The device used to measure the distance travelled by a vehicle is called an odometer.
$(c)$ Yes,the displacement of a moving object can be zero. This happens if the object returns to its initial starting position after completing its motion,as displacement is the shortest distance between the initial and final positions.
Slope $= \frac{\text{Change in velocity}}{\text{Time taken}} = \frac{v - u}{t}$.
Therefore,$a = \frac{v - u}{t}$,which gives $at = v - u$,or $v = u + at$.
$(b)$ The device used to measure the distance travelled by a vehicle is called an odometer.
$(c)$ Yes,the displacement of a moving object can be zero. This happens if the object returns to its initial starting position after completing its motion,as displacement is the shortest distance between the initial and final positions.
Explore More
Similar Questions
$A$ train is travelling at a speed of $90\, km\, h^{-1}$. Brakes are applied so as to produce a uniform acceleration of $-0.5\, m\, s^{-2}$. Find how far the train will go before it is brought to rest. (in $, m$)
Difficult
View SolutionDistinguish between the terms speed and velocity.
Medium
View SolutionThe velocity$-$time graph of a truck is plotted below.
$(a)$ Calculate the magnitude of displacement of the truck in $15$ seconds.
$(b)$ During which part of the journey was the truck decelerating?
$(c)$ Calculate the magnitude of average velocity of the truck.
$(a)$ Calculate the magnitude of displacement of the truck in $15$ seconds.
$(b)$ During which part of the journey was the truck decelerating?
$(c)$ Calculate the magnitude of average velocity of the truck.
Medium
View SolutionAn object is moving along a straight line with uniform acceleration. The following table gives the velocity of the object at various instants of time.
Time $(s)$ $0$ $1$ $2$ $3$ $4$ $5$ $6$ Velocity $(m s^{-1})$ $2$ $4$ $6$ $8$ $10$ $12$ $14$
Plot the graph.
From the graph:
$(i)$ Find the velocity of the object at the end of $2.5 \ s$.
$(ii)$ Calculate the acceleration.
$(iii)$ Calculate the distance covered in the last $4 \ s$.
| Time $(s)$ | $0$ | $1$ | $2$ | $3$ | $4$ | $5$ | $6$ |
| Velocity $(m s^{-1})$ | $2$ | $4$ | $6$ | $8$ | $10$ | $12$ | $14$ |
Plot the graph.
From the graph:
$(i)$ Find the velocity of the object at the end of $2.5 \ s$.
$(ii)$ Calculate the acceleration.
$(iii)$ Calculate the distance covered in the last $4 \ s$.
Medium
View SolutionThe velocity-time graph (Fig.) shows the motion of a cyclist. Find $(i)$ its acceleration $(ii)$ its velocity and $(iii)$ the distance covered by the cyclist in $15\,s$.
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