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A five-tonne truck and a two-quintal car are moving with an equal velocity. After applying the brake, what will happen?
1. The truck will stop covering more distance
2. The car will stop covering more distance
3. Both will stop covering same distance
4. Distance covered before stop depends upon the driver

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Correct Answer - Option 1 : The truck will stop covering more distance

Concept:

  • Force (F) is defined as pushing or pulling of an object, due to which the motion of the body will be changed.
  • Mathematically, a force can be written as:

F = ma

Where m = mass of the body and a = acceleration of the body

  • Force is a vector quantity.
  • SI Unit of force is Newton.

There are three equations of motion that can be used to derive components such as displacement(s), velocity (initial and final), time(t), and acceleration(a).
The following are the three equation of motion:

  • First Equation of Motion:

v = u + at

  • Second Equation of Motion:

s = u t + \({1 \over 2}\) at2

  • Third Equation of Motion:

v2 = u+ 2 as
Where the initial velocity is u, acceleration is denoted as a time period is denoted as t, the final velocity is denoted as v, and the distance traveled is denoted as s.

Explanation:

The formula of force is -

F = ma

  • The stopping force applied to the truck and the car is the same so,

Ft = Fc    (  Ft is stopping force applied to the truck and Fis the stopping force applied to the car)

  • But, the mass of the car and the truck is different, mt > m(mt is the mass of the truck and m is the mass of the car)
  • So, in order to stand by the situation where the force applied through a break on the truck and the car be same, the acceleration of the truck will be lesser than that of the car

a> at                ---------------------- 1        

(at is the acceleration of the truck and ac  is the acceleration of the car)

  • Now, the initial velocity, u, is the same for both the car and the truck, as said in the question!
  • The final velocity, v, is zero for both as breaks are being applied and both the truck and the car are coming to rest
  • St is the distance covered by the truck and Sc be the distance covered by the car.
  • Applying equation, v2 - u2 = 2aS (one of the three equations of motion),

for truck, 

0 - u= 2 (-at) St

S= u2/2 at      ---------------------- 2  

for car, 

0 - u= 2 (-ac) Sc

Sc = u2/2ac     ---------------------- 3  

(The negative sign is being used for acceleration because deacceleration is taking place)

  • Dividing equation 2 by equation 3

St/Sc = ac/at > 1 (from equation 1)

So, St/Sc > 1

Hence, St > Sc

  • Distance traveled by truck is greater than distance traveled by car.

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