A car is travelling at a speed of 90 km/h. Brakes are applied so as to produce a uniform acceleration of – 0.5 m/s2. Find how far the car will go before it is brought to rest?
Answers
Answer- The above question is from the chapter 'Kinematics'.
Some important terms and formulae:-
1. Velocity- It is the displacement per unit time.
S.I. Unit of Velocity- m/s
It is a vector quantity as it possesses magnitude and direction.
2. Acceleration- It is the rate of change of velocity.
S.I. Unit of Acceleration- m/s²
It is also a vector quantity.
Negative acceleration is called retardation.
3. Distance- It is the path length transversed by an object.
S.I. Unit of Distance- m
It is a scalar quantity.
4. Displacement- It is the shortest distance between the initial and final point.
S.I. Unit of Displacement- m
It is a vector quantity.
5. Equations for uniformly accelerated motion-
Let u = Initial velocity of a particle
v = Final velocity of a particle
t = Time taken
s = Distance travelled in the given time
a = Acceleration
1) v = u + at
2) s = at² + ut
3) v² - u² = 2as
Given question: A car is travelling at a speed of 90 km/h. Brakes are applied so as to produce a uniform acceleration of - 0.5 m/s². Find how far the car will go before it is brought to rest.
Answer: u = 90 km/hr = 25 m/s
v = 0 m/s
a = - 0.5 m/s²
s = ?
Using 3rd equation of motion i.e. v² - u² = 2as, we get,
0² - 25² = 2 × - 0.5 × s
- 625 = - s
s = 625 m
∴ Distance that the car will cover before it is brought to rest = 625 m
Answer:
Explanation:
Given:-
Initial speed of the train, u = 90 km/h = 25 m/s
The final speed of the train, v = 0
Acceleration = - 0.5 m/s²
To Find:-
Distance acquired
Formula to be used:-
Third equation of motion:
v² = u² + 2 as
Solution:-
Putting all the value, we get
v² = u² + 2as
⇒ (0)² = (25)² + 2 (- 0.5) s
⇒ s = 625 m
Hence, The train will cover a distance of 625 m before coming to rest.
Important terms:-
Distance - Distance is the actual length of the path covered by a body during the whole journey, without taking into consideration its direction. It is a scalar quantity.
Displacement - Displacement is the distance in a particular direction. It is a vector quantity.
Initial speed - Initial speed is that speed with which a body starts its motion in the beginning. It is denoted by u.
Final speed - Final speed is that speed which is acquired by the body after its start. It is denoted by v.
Note* - Both are zero when a body finally come to rest or starts from rest.
Retardation - When the final speed of a body is less than its initial speed, the body is said to be retardation. Retardation can also be expressed as acceleration with a minus (-) sign.