Question

Ques-) A car weighing 1000 kg and travelling at 30m/s stops at a distance of 50m decelerating uniformly.what is the force exerted on it by the brakes? what is the work done by the brakes?
(I know it's ans but tell me the full forms)
Ans-) m=1000kg
u=30m/s
S=50m
V=0
a=?
F=?
W=?
​

Answer 1

Given:-

• Mass of car ,m = 1000 kg

• Initial velocity ,u = 30m/s

• Final velocity,v = 0m/s

• Distance travelled ,s = 50 m

To Find:-

• Work done by brake ,W

Solution:-

Firstly we calculate the acceleration of the car.

Using 3rd Equation of Motion

• v² = u² +2as

v is the final velocity

a is the acceleration

u is the initial velocity

s is the distance travelled

Substitute the value we get

→ 0² = 30² + 2×a × 50

→ 0 = 900 + 100×a

→ a = -900/100

→ a = -9m/s²

Here, negative sign show retardation

Therefore, the acceleration of the car is 9m/s²

Now, Calculating the work done

• W = Fs

Where,

W is the Work Done

F is the force

s is the displacement

Substitute the value we get

→ W = ma × s ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ (F = ma)

Here, F = ma

where

F is the Force

m is the mass

a is the acceleration

→ W = 1000 × 9 × 50

→ W = 1000 × 450

→ W = 450000 J

→ W = 4.5 × 10⁵ J or 450 KJ

Therefore, the work done by the. brake is 450 KiloJoules .

Answer 2

ㅤㅤㅤㅤㅤㅤㅤㅤ$\large \bigstar \rm { \underline \red{ \: \: \: \: \: \: \: \: \: GiVeN \: \: \: \: \: \: \: \: \: \: }} \bigstar$

• Mass of the car, m ❥ 1000 kg

• Initial velocity , u ❥ 30 m/s

• Final velocity , v ❥ 0 m/s

• Distance travelled , s ❥ 50 m

ㅤㅤㅤㅤㅤㅤㅤㅤ$\large \bigstar \rm { \underline \red{ \: \: \: \: \: \: \: \: \: To\: FiNd \: \: \: \: \: \: \: \: \: \: }} \bigstar$

• Work done, W ❥ ?

ㅤㅤㅤㅤㅤㅤㅤㅤ$\large \bigstar \rm { \underline \red{ \: \: \: \: \: \: \: \: \: FoRmuLa\: \: \: \: \: \: \: \: \: \: }} \bigstar$

$\: \: \: \: \: \: \large \bigstar\rm {\boxed {\green{\boxed{{v}^{2} = {u}^{2} + 2as}}}} \bigstar$

$\: \: \: \: \: \: \large \bigstar\rm {\boxed {\green{\boxed{W = m × a × s}}}} \bigstar$

ㅤㅤㅤㅤㅤㅤㅤㅤㅤㅤㅤㅤㅤㅤㅤㅤㅤ$\large \bigstar \rm { \underline \red{ \: \: \: \: \: \: \: \: \: SoLuTiOn \: \: \: \: \: \: \: \: \: \: }} \bigstar$

$: \implies\rm \: { {0}^{2} = {30}^{2} + 2 \times \: a \times 50}$

$: \implies \rm0 = 900 + 100 \times a \\ \\ : \implies \rm \: - 100a = 900 \\ \\ : \implies \rm \: a = \cancel\frac{900}{ - 100} \\ \\ : \implies \rm \: a = - 9m/s$

• it will be 9 m/s as it is mentioned about brakes.

ㅤㅤㅤㅤㅤㅤㅤㅤ$\large \bigstar \rm { \underline \red{ \: \: \: \: \: \: \: \: AnOtHer \: FoRmuLa\: \: \: \: \: \: \: \: \: \: }} \bigstar$

$\large \bf \red{w = m \times a \times s}$

ㅤㅤㅤㅤㅤㅤㅤ❥ W = 1000 × 9 × 50

ㅤㅤㅤㅤㅤㅤㅤ❥ W = 1000 × 450

ㅤㅤㅤㅤㅤㅤㅤ❥ W = 450000 J

ㅤㅤㅤㅤㅤㅤㅤ❥ W = 450 KJ

ㅤㅤㅤㅤㅤㅤㅤㅤㅤㅤㅤㅤㅤㅤㅤㅤㅤ$\large \bigstar \rm { \underline \red{ \: \: \: \: \: \: \: \: \: ThEreFoRe\: \: \: \: \: \: \: \: \: \: }} \bigstar$

• Work done by Brakes = 450 KJ