The brakes applied to a car produce an acceleration of 6 m s-2 in the opposite direction to the motion. If the car takes 2 s to stop after the application of brakes, calculate the distance it travels during this time.
Answers
Given :
• The brakes applied to a car produce an acceleration of 6 m/s² in the opposite direction to the motion.
• The car takes 2 s to stop after the application of brakes.
To find :
• Distance travelled by the car
Solution :
We have,
• Acceleration of the car = - 6 m/s² [Here, we have acceleration as negative because it is acting in the opposite direction to motion.]
• Final velocity of the car = 0 m/s
• Time = 2 seconds
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Firstly, we will find the initial velocity of the car by using the first equation of motion. Then after getting its value we can easily calculate the distance travelled by using the third equation of motion.
First equation of motion :-
- v = u + at
where,
• v denotes the final velocity
• u denotes the initial velocity
• a denotes the acceleration
• t denotes the time
Substituting the given values :-
⟶ 0 = u + (- 6)(2)
⟶ 0 = u - 12
⟶ 12 = u
Therefore, the initial velocity of the car = 12 m/s
Third equation of motion :-
- v² - u² = 2as
where,
• s denotes the distance/displacement
Substituting the given values :-
⟶ (0)² - (12)² = 2(- 6)(s)
⟶ - 144 = - 12 × s
⟶ 144 = 12 × s
⟶ 144/12 = s
⟶ 12 = s
Therefore, the distance travelled by the car = 12 m