Question

A car weighing 9800 N is moving with a speed of 40 km/h.
On the application of the brakes It comes to rest after travel-
ling a distance of 50 metres. Calculate the average retarding
force.

Answer 1

Answer:

• The average retarding force acting on the Car will be -1234.568 N.

Explanation:

Given

• Weight of Car, W = 9800 N
• Initial velocity of Car, u = 40 km/h = 40*5/18 m/s = 100/9  m/s
• Final velocity of Car, v = 0
• Distance covered by Car before coming to rest and after applying brakes, s = 50 m

To find

• Average retarding force, F =?

Formulae required

• Third equation of motion

       2 a s = v² - u²

• Formula for weight of a body

       W = m g

• Newton's second law of motion

        F = m a

[ Where a is acceleration, s is distance covered, v is final velocity, u is initial velocity, W is weight, m is mass, g is acceleration due to gravity, F is force, and m is mass of body ]

Solution

• Let, mass of Car = m
• and, Acceleration of car = a

Using formula to calculate Weight of body

→ W = m g

[ taking g = 9.8 m/s² ]

→ 9800 = (m) · (9.8)

→ m = 9800 / 9.8

→ m = 1000 kg

Now using third equation of motion

→ 2 a s = v² - u²

→ 2 a · ( 50 ) = ( 0 )² - ( 100/9 )²

→ 100 a = -10000/81

→ a = -10000/8100

→ a = -100/81  m/s²    

Now, by newton's second law of motion

→ F = m a

→ F = ( 1000 ) · ( -100/81 )

→ F = ( -100000 ) / 81

→ F = -1234.568 N    [approx.]

Therefore,

• The average retarding force acting on the Car will be -1234.568 N.

Answer 2

Given : -

• A car weighing 9800 N is moving

• a speed of 40 km/h.

• On the application of the brakes It comes to rest after travel-ling a distance of 50 metres.

To Find : -

• Calculate the average retarding care force.

Solution : -

Applying brake final speed will be zero

v = 40 km/h =11.11 m/s

a = v²/2s

Putting all values

a = 11.11²/ 2 × 50

a = 1.234

The mass of the car:

m= w / g

putting all values

9800/9.8

1000 kg

The speed of car:

a = v²/2d

To change km/h into m/s we have to multiply by 5/18

40 × 5 / 18

100/9 m/s

The average retarding force:

a = m × v^²/2d

putting all values

A=M×v²/2d =1000× (100/9)²/ 2/50

Hence the average retarding force. is 1234.57N