Question

You move along $+x$ direction through a distance of $10\,m$ and then move back through a distance of $4\,m$ Repeat It four times during ten minutes, find the:
(A) total
$(i)$ Distance
$(ii)$ Displacement and
(B) average
$(i)$ speed,
$(ii)$ velocity.

Answer 1

Hint: We come across scenarios where we need to determine which of the two or more things is going faster. The faster of the two, one can easily tell if they are going in the same direction on the same lane. But if their direction of motion is in the opposite direction, then deciding the fastest is difficult.

Formula used:
\[speed\; = \dfrac{Distance}{Time}\]
\[Velocity\; = \dfrac{Displacement}{Time}\]
\[distance\; = \;speed\; \times \;time.\]
Displacement can be calculated by measuring the final distance away from a point, and then subtracting the initial distance.
${\text{displacement = (covered}}\,{\text{distance - starting}}\,{{distance) \times time}}$
Displacement is key when determining velocity
Velocity = displacement/time

Complete step by step solution:
Let covered distance is $10\,m$ ,back through a distance $4\,m$
We find the total distance, displacement,
Then we find Average speed and velocity,
Let take,
$(i)$ ${\text{Distance}} = \left( {10 + 4} \right) \times 10time$
On simplifying, We get,
$\Rightarrow$ ${\text{Distance}} = 14 \times 10$
Multiplying the above equation,
Here,
Distance is $140\,m$
$(ii)$ Displacement
$Displacement = \left( {10 - 4} \right) \times 10$
On simplifying, We get,
$\Rightarrow$ $Displacement = 6 \times 10$
Multiplying the above equation,
Here, Displacement is $60\,\,m$
$(ii)\,average\,Speed = \dfrac{{Dis\tan ce}}{{time}}$
Substituting the given value in above equation,
We get, $Average\,speed = \dfrac{{140}}{{10\min }}$
We know that one minute is equal to sixty seconds,
Here, $Average\,speed = \dfrac{{140}}{{10 \times 60}}$
Then, performing the dividing operation,
Cancel the specific numbers,
We get, \[Average\,speed = \dfrac{{14}}{{0.1}}m/s\]
$(ii)$ $Average\,velocity = \dfrac{{Displacement}}{{time}}$
Substituting the given value,
\[Average\,velocity = \dfrac{{60}}{{10 \times 60}}\]
On simplifying, We get,
$\Rightarrow$ $0.1\,m/s$
Thus, the Average velocity is $0.1\,m/s$
Hence, The total Distance is $140\,m$
The total Displacement is $60\,\,m$
Average speed is \[\dfrac{{14}}{{0.1}}m/s\]
Average velocity is $0.1\,m/s$.

Note: For most of us, speed and velocity can be a little confusing. This speed gives us an idea of how quickly an object moves, whereas speed not only tells us its speed but also tells us the direction in which the body moves. We can define velocity as a function of the distance traveled, while velocity is a displacement function.