Question

If a car running with velocity 72 km/h is to be stopped within 100m. How much force is to applied by the break if the mass of car is 100kg.​

Answer 1

Given data : If a car running with velocity 72 km/hr is to be stopped within 100 m and mass of car is 100 kg.

To find : How much force is to applied by the break of the car ?

Solution : Now, according to given data,

⟹ Initial velocity of car ( u ) = 72 km/hr

⟹ Final velocity of car ( v ) = 0 (Car stopped after braking)

⟹ Mass of car ( m ) = 100 kg

⟹ Distance covered by car ( s ) = 100 m

Here, we know,

⟹ 72 km/hr = [72 * 1000]/[60 * 60] m/s

⟹ 72 km/hr = 72000/3600 m/s

⟹ 72 km/hr = 720/36 m/s

⟹ 72 km/hr = 20 m/s

Hence, Initial velocity of car ( u ) = 20 m/s

Now, by kinematical equation

⟹ v² = u² + 2 * a * s

where ‘ a ’is acceleration of the car.

⟹ 0 = (20)² + 2 * a * 100

⟹ 0 = 400 + 2 * a * 100

⟹ 0 - 400 = 2 * a * 100

⟹ - 400 = 200 * a

⟹ a = - 400/200

⟹ a = - 2 m/s²

Now, to find force is to applied by the break of the car,

we use formula of force :

⟹ Force = mass * acceleration

⟹ F = m * a

⟹ F = 100 * ( - 2 )

⟹ F = - 200 N

Answer : Force is to applied by the break of the car is - 200 N.

More info : Breaks of the car tries to decrease the displacement by acting in the direction opposite to displacement. So we get the force in the negative sign.

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