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

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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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