Question

A truck is moving with a velocity of 2m/s From A to B , at B, there is a rectangle road BCDE where, BC = 20m and CD = 40m.
If the truck travels 10 rounds of the rectangle and reaches E, so at what speed should the truck should travel so the the velocity from A to E is 2m/s

Answer 1

Given :

• Velocity of Truck A from A to B = 2m/s
• Dimensions of the rectangle Road:

1. BC = DE = 20m
2. CD = EB = 40m

• Velocity required from A to E = 2m/s
• Note, Yo have not given AB , so I will take it as 10m

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To Find :

• At what Speed should the truck be driven, so that the average Velocity from A to E is 2m/s only?

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Concept :

1] Velocity : It is the rate of Displacement with respect to time. As we know, Displacement is the shortest distance between initial and final position. It involves a direction.

Velocity is a Vector quantity.

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2] Speed : It is the rate of Distance moved with respect to time. It just needs the total Distance moved and the time. Speed doesn't involve direction . Speed is Scalar Quantity.

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•So, as we got, velocity is Always considered in straight line, so first we will calculate Displacement of the truck and then the time to reach their with the given Velocity.

• Then, we will calculate the total Distance covered by the truck and divide it by the time we got for Find the required Answer :)

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Formula To Be Applied:

• Speed = Distance/ time
• Velocity = Displacement/time
• Time = Displacement/Velocity

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Solution :

Given, Displacement from A to B = 10m

Displacement from B to E = 40m

So, total Displacement of truck = 10m+40m = 50m

(As they are in straight line)

So, With the velocity given = 2m/s ,

So, Time taken :

$\displaystyle \rm \implies t = \frac{displacement}{velocity}$

$\displaystyle \rm \implies t = \frac{50}{2}$

$\displaystyle \rm \implies t = 25s$

Hence, The time taken by truck to reach A to E = 25s

But given, The truck is moving with a velocity of 2m/s from A to B , so we will exclude the time taken from A to B .

So, time taken from A to B = 10/2 = 5s

So, Time taken to cover the rectangle Road = 20s

But, As Given, The truck takes 10 round of the rectangle Road and reaches E,

So, Distance Travelled By truck = 10(Perimeter of BCDE ) - BE

So, Distance travelled :

$\displaystyle \rm \implies d = 10(2 \times 60) - 40$

$\displaystyle \rm \implies d = 10(120) - 40$

$\displaystyle \rm \implies d = 1200 - 40$

$\implies \displaystyle \rm \: d =1160m$

Hence, Distance travelled by truck on the rectangle Road = 1160m

So, Speed of Truck (Rectangle Road ) :

$\displaystyle \rm \implies s = \frac{distance}{time}$

$\displaystyle \rm \implies s = \frac{1160}{20}$

$\red { \underline{ \boxed{\implies \displaystyle \rm speed = 58mps}}}$

So, Speed Required = 58 m/s

So, the truck needs to travel With a velocity of 58m/s To remain at the same velocity as With A to B .

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Final Answer :

The Speed required = 58m/s

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