Question

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A 500 kg truck is moving at a speed of 90m/s stops after covering some distance the force applied by brakes is 27000 N . Compute the distance covered and work done by this Force...?

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Answer 1

Given :

Mass of truck = 500kg

Initial velocity = 90m/s

Force applied by brakes = 27000N

Final velocity = zero

To Find :

Distance covered by truck before coming to rest and work done by force.

Solution :

❒ First of all we need to find acceleration of the truck.

As per newton's second law of motion, force is measured as the product of mass and acceleration$.$

Mathematically, F = m × a

• F denotes force
• m denotes mass
• a denotes acceleration

By substituting the given values;

➠ F = m × a

➠ 27000 = 500 × a

➠ a = 270/5

➠ a = 54 m/s²

Here acceleration will be negative as velocity decreases with time.

Therefore, a = -54 m/s²

★ Distance covered by car can be calculated by using third equation of kinematics.

➛ v² - u² = 2as

➛ 0² - 90² = 2(-54) × s

➛ s = -8100 / -108

➛ s = 75 m

★ Work done by force :

➙ W = -F d

Here negative sign indicates that, force is acting in opposite direction. It is called retarding force.

➙ W = -27000 × 75

➙ W = 2,025,000

➙ W = -2.025 MJ (1MJ = 10⁶J)

Answer 2

Question :-

A 500 kg truck is moving at a speed of 90m/s stops after covering some distance the force applied by brakes is 27000 N . Compute the distance covered and work done by this Force...?

Answer :-

• Distance = 75 m.
• Work Done = -2.025 MJ.

Given : -

• u = 90m/s
• v = 0 m
• M = 500 kg
• F = 27000N

Here ,

➤ " u " = Initial velocity

➤ " v " = Final velocity

➤ " m " = Mass of the body ( truck )

➤ " F " = Force exerted .

Have to Find :-

• Whats the Distance covered by truck ?
• How much work done ?

Calculations :-

We know the formula to find distance :-

{ v² - u² = 2as }

➤ " u " = Initial velocity

➤ " v " = Final velocity

➤ " a " = acceleration

➤ " s " = Distance

In order to find the distance first we need to know acceleration :-

So , let's Calculate the acceleration

As we all know

• F = ma

Where ,

➤ " a " = acceleration

➤ " m " = Mass of the body

➤ " F " = Force exerted

Therefore , substituting the values in the above formula , we get :-

Note :- Acceleration will remain negative because in this condition velocity decreasing time by time .

27000 = 500 × a

a = 270/5

a = 54 m/s²

Now , we got the acceleration .

So , simply using third equation of motion to get distance .

↬ v² - u² = 2as

↬ 0² - 90² = 2(-54) × s

↬ s = -8100 / -108

↬ s = 75 m

Hence , the second of Question i.e, work done .

we know the formula

Note :- If force act in opposite direction then it is referred as retardation and because of this ,then we take force negative .

↬ W = - F d

↬( -27000 ) * 75

↬ 2,025,000

Therefore ,

$Work \: Done$ = -2.025 MJ