A train starting from rest attains a velocity of 90 km/h in 5 minutes. Assuming that the acceleration is uniform,
what is the distance traveled by the train in this 5 minutes.?
PLS CAN I GET THIS QUICK...
Answers
Required Answer :
The distance travelled by the train = 3750 m
Given :
- Initial velocity of the train = 0 m/s
- Time = 5 minutes
- Final velocity of the train = 90 km/h
To find :
- Distance travelled by the train
Solution :
Firstly, we shall convert the final velocity and the time into m/s and seconds respectively.
→ Time = 5 minutes
As we know,
1 min = 60 s
→ Time = 5 × 60
→ Time = 300 s
→ Final velocity = 90 km/h
To convert the value of final velocity from km/h into m/s, multiply it by 5/18.
→ Final velocity = 90 × 5/18
→ Final velocity = 5 × 5
→ Final velocity = 25 m/s
Now, we will use the first equation of motion to calculate the acceleration.
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
we have,
- v = 25 m/s
- u = 0 m/s
- t = 300 s
Substituting the given values :-
→ 25 = 0 + (a)(300)
→ 25 = a × 300
→ 25/300 = a
→ 5/60 = a
→ 1/12 = a
Therefore, the acceleration of the train = 1/12 m/s²
By using the third equation of motion, we will calculate the distance travelled by the train.
Third equation of motion :-
- v² - u² = 2as
where,
- v denotes the final velocity
- u denotes the initial velocity
- a denotes the acceleration
- s denotes the distance/displacement
We have,
- v = 25 m/s
- u = 0 m/s
- a = 1/12 m/s²
Substituting the given values :-
→ (25)² - (0)² = 2(1/12)(s)
→ (25)² = 2 × 1/12 × s
→ 625 = 1/6 × s
→ 625 × 6 = s
→ 3750 = s
Therefore, the distance travelled by the train = 3750 m