Question

A car running at 72 kmph is slowed down to 18 kmph by the application of brakes
over a distance of 20 m. The deceleration of car is
[]
A) 9.375 m/s2 B) 6.375 m/s2 C) 3.375 m/s D) 0.375 m/s2​

Answer 1

$\displaystyle\large\underline{\sf\red{Given}}$

✭ Initial Velocity (u) = 72 km/h

✭ Final Velocity (v) = 18 km/h

✭ Distance (s) = 20 m

$\displaystyle\large\underline{\sf\blue{To \ Find}}$

◈ The Deceleration of the car?

$\displaystyle\large\underline{\sf\gray{Solution}}$

So here Deceleration means negative Acceleration that is the acceleration is in the opposite direction to the motion and so that it's Speed reduces

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$\underline{\bigstar\:\textsf{According to the given Question :}}$

So here we shall use the third Equation of motion, that is,

$\displaystyle\sf \underline{\boxed{\sf v^2-u^2 = 2as}}$

• v = 18 km/h
• u = 72 km/h
• s = 20 m

So we see that the speeds are in km/h so on converting them,

➝ $\displaystyle\sf v = 18\times \dfrac{5}{18}$

➝ $\displaystyle\sf \purple{Final \ Velocity = 5 \ m/s}$

»» $\displaystyle\sf u = 72\times \dfrac{5}{18}$

➝ $\displaystyle\sf \orange{Initial \ Velocity = 20 \ m/s}$

Now the Deceleration will be,

➳ $\displaystyle\sf v^2-u^2 = 2as$

➳ $\displaystyle\sf 5^2-20^2 = 2\times a\times 20$

➳ $\displaystyle\sf 25-400 = 40a$

➳ $\displaystyle\sf -375 = 40a$

➳ $\displaystyle\sf \dfrac{-375}{40} = a$

➳ $\displaystyle\sf \pink{Deceleration = 9.375 \ m/s^2}$

$\displaystyle\sf \underline{\therefore Answer \ is \ Option \ A}$

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Answer 2

Answer :-

★ The deceleration of the car is = Option A) 9.375 m/s²

★ Concept :

• In this question, the concept used is retardation or simply to say negative of acceleration. Here, we are gonna take negative value of acceleration in order to find deceleration.

★ Solution :-

Given,

• Initial velocity of the car = 'u'

= 72 Km/H = 20 m/s

• Final velocity of the car = 'v' = 18 Km/H = 5 m/s

• Distance covered during deceleration = 's' = 20 m

▶ To Find = Deceleration

Let the deceleration be 'a'. Then,

Using the Newton's Third Equation of Motion,

✏ v² - u² = 2as

By applying values, we get,

✏ (5)² - (20)² = 2 × a × 20

✏ (25) - (400) = 40 × a

✏ a × 40 = - 375

✏ $a \: \: = \: \: \dfrac{ - \: 375}{40}$

✏ a = 9.375 m/s

On rechecking the values of units, we get,

a = 9.375 m / s²

Hence, deceleration of car = 9.375 m/s²

So the correct answer is Option A).

★ More to know :

• • Acceleration = The rate of change of velocity of an object is called its acceleration.

Acceleration = Change in Velocity / Time

Acceleration is a vector quantity. Its SI unit is m/s² and dimensional formula is [L¹ / T² ] .

• • Uniform Acceleration = If the velocity of an object changes by equal amounts in equal intervals of time, however small these intervals may be, then the object is said to move with uniform or constant acceleration.

• • Variable Acceleration = If the velocity of an object changes by unequal amounts in equal intervals of time, then the object is said to be ib variable acceleration.

• • Positive Acceleration = If the velocity of an object increases with time, its acceleration is positive.

• • Negative Acceleration = If the velocity of an object decreases with time, tye acceleration is negative. Negative acceleration is also called 'retardation' or 'declaration'.

Note* Whenever we are changing units from Km/H to m/s, we can do it by multiplying the measurement in Km/H by 5/18 and by dividing by 5/18 when we are changing from m/s to Km/H.