$A$ body can have zero average velocity but not zero average speed. Justify this statement by giving an example.
(N/A) Average velocity is defined as the total displacement divided by the total time taken. Since displacement is a vector quantity,if an object returns to its starting point,the total displacement becomes $0$,resulting in an average velocity of $0$.
Average speed is defined as the total distance traveled divided by the total time taken. Since distance is a scalar quantity and represents the total path length,it cannot be $0$ for a moving object.
Example: Consider an object moving along a circular path of radius $r$. If the object completes one full revolution,the total displacement is $0$,so the average velocity is $0$. However,the total distance traveled is equal to the circumference of the circle,which is $2 \pi r$. Thus,the average speed is $\frac{2 \pi r}{t}$,where $t$ is the time taken.
Average speed is defined as the total distance traveled divided by the total time taken. Since distance is a scalar quantity and represents the total path length,it cannot be $0$ for a moving object.
Example: Consider an object moving along a circular path of radius $r$. If the object completes one full revolution,the total displacement is $0$,so the average velocity is $0$. However,the total distance traveled is equal to the circumference of the circle,which is $2 \pi r$. Thus,the average speed is $\frac{2 \pi r}{t}$,where $t$ is the time taken.
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Similar Questions
Derive the following equations for a uniformly accelerated motion:
$(i)$ $v = u + at$
$(ii)$ $S = ut + \frac{1}{2}at^2$
$(iii)$ $v^2 - u^2 = 2aS$, where the symbols have their usual meanings.
$(i)$ $v = u + at$
$(ii)$ $S = ut + \frac{1}{2}at^2$
$(iii)$ $v^2 - u^2 = 2aS$, where the symbols have their usual meanings.
Difficult
View SolutionAccount for the following:
$(a)$ Name the quantity which is measured by the area occupied below the velocity$-$time graph.
$(b)$ Give an example of an object moving in a certain direction with acceleration in the perpendicular direction.
$(c)$ Under what condition is the magnitude of average velocity of an object equal to its average speed?
$(d)$ Give an example of uniformly accelerated motion.
$(e)$ $A$ body is moving along a circular path of radius $r$. What will be the distance and displacement of the body when it completes half a revolution?
$(a)$ Name the quantity which is measured by the area occupied below the velocity$-$time graph.
$(b)$ Give an example of an object moving in a certain direction with acceleration in the perpendicular direction.
$(c)$ Under what condition is the magnitude of average velocity of an object equal to its average speed?
$(d)$ Give an example of uniformly accelerated motion.
$(e)$ $A$ body is moving along a circular path of radius $r$. What will be the distance and displacement of the body when it completes half a revolution?
Medium
View SolutionThe driver of a train $A$ travelling at a speed of $54\, km\, h^{-1}$ applies brakes and retards the train uniformly. The train stops in $5\, s$. Another train $B$ is travelling on the parallel track with a speed of $36\, km\, h^{-1}$. This driver also applies the brakes and the train retards uniformly. The train $B$ stops in $10\, s$. Plot the speed-time graph for both the trains on the same paper. Also,calculate the distance travelled by each train after the brakes were applied.
Medium
View Solution$(a)$ Derive the second equation of motion $S = ut + \frac{1}{2}at^2$ graphically,where the symbols have their usual meanings.
$(b)$ $A$ car accelerates uniformly from $18 \text{ km h}^{-1}$ to $36 \text{ km h}^{-1}$ in $5 \text{ s}$. Calculate the acceleration and the distance covered by the car in that time.
$(b)$ $A$ car accelerates uniformly from $18 \text{ km h}^{-1}$ to $36 \text{ km h}^{-1}$ in $5 \text{ s}$. Calculate the acceleration and the distance covered by the car in that time.
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View SolutionWrite any two equations of motion for a body having uniform acceleration.
Easy
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