a car moving with velocity 60km/hr is stopped by applying brakes in a distance 5m. if the mass of car is 1000kg. what average force is applied on it.?
Answers
Given :
• A car moving with velocity 60km/hr is stopped by applying brakes in a distance 5 m.
• The mass of the car is 1000 kg.
To find :
• Average force applied on it
Solution :
To find the force applied on the car, firstly we shall calculate the acceleration of the car by using the third equation of motion.
We have,
Initial velocity of the car = 60 km/h
Final velocity of the car = 0 m/s [Because it comes to rest after brakes are applied.]
Distance travelled by the car = 5 m
Mass of the car = 1000 kg
Before calculating the acceleration we will convert the initial velocity of the car from km/h into m/s.
To convert the value from km/h into m/s mulitply it by 5/18.
⟶ Initial velocity = 60 × 5/18
⟶ Initial velocity = 300/18
Therefore, the initial velocity of the car = 300/18 m/s
Third equation of motion :-
v² - u² = 2as
where,
v = Final velocity
u = Initial velocity
a = Acceleration
s = distance/displacement
Substituting the given values :-
⟶ (0)² - (300/18)² = 2(a)(5)
⟶ - 90,000/324 = 10 × a
⟶ - 90,000/324 × 1/10 = a
⟶ - 9000/324 = a
⟶ - 27.78 = a
Therefore, the acceleration of the car = - 27.78 m/s²
Formula to calculate force,
⟶ Force = ma
where,
- m = mass
- a = acceleration
Substituting the given values :-
⟶ Force = 1000 × (- 27.78)
⟶ Force = - 27780
Therefore, the force = - 27780 N