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A train starting from rest attains a velocity of 72 km/h in 5 minutes. Assuming that the acceleration is uniform, find the distance travelled by the train for attaining this velocity
- a)5km
- b)7km
- c)6km
- d)3km
Correct answer is option 'D'. Can you explain this answer?
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Most Upvoted Answer
A train starting from rest attains a velocity of 72 km/h in 5 minutes....
Given:
Initial velocity (u) = 0 km/h
Final velocity (v) = 72 km/h
Time (t) = 5 minutes = 5/60 hours
Formula:
The formula to calculate distance (s) using uniform acceleration is:
s = (v^2 - u^2) / (2a)
where v is the final velocity, u is the initial velocity, a is the acceleration, and s is the distance.
Calculation:
We need to find the distance traveled by the train for attaining a velocity of 72 km/h.
We know that the initial velocity u is 0 km/h, so u^2 = 0.
Plugging the given values into the formula:
s = (v^2 - u^2) / (2a)
s = (72^2 - 0) / (2a)
s = 5184 / (2a)
We need to find the value of a.
Acceleration (a) can be calculated using the formula:
a = (v - u) / t
Plugging the given values into the formula:
a = (72 - 0) / (5/60)
a = 72 / (5/60)
a = 720 / 5
a = 144 km/h^2
Now, substitute the value of a in the equation for distance:
s = 5184 / (2 * 144)
s = 5184 / 288
s = 18 km
Therefore, the distance traveled by the train to attain a velocity of 72 km/h is 18 km.
The correct option is (d) 3 km. However, this answer seems to be incorrect based on the calculations. The correct answer should be (c) 6 km.
Initial velocity (u) = 0 km/h
Final velocity (v) = 72 km/h
Time (t) = 5 minutes = 5/60 hours
Formula:
The formula to calculate distance (s) using uniform acceleration is:
s = (v^2 - u^2) / (2a)
where v is the final velocity, u is the initial velocity, a is the acceleration, and s is the distance.
Calculation:
We need to find the distance traveled by the train for attaining a velocity of 72 km/h.
We know that the initial velocity u is 0 km/h, so u^2 = 0.
Plugging the given values into the formula:
s = (v^2 - u^2) / (2a)
s = (72^2 - 0) / (2a)
s = 5184 / (2a)
We need to find the value of a.
Acceleration (a) can be calculated using the formula:
a = (v - u) / t
Plugging the given values into the formula:
a = (72 - 0) / (5/60)
a = 72 / (5/60)
a = 720 / 5
a = 144 km/h^2
Now, substitute the value of a in the equation for distance:
s = 5184 / (2 * 144)
s = 5184 / 288
s = 18 km
Therefore, the distance traveled by the train to attain a velocity of 72 km/h is 18 km.
The correct option is (d) 3 km. However, this answer seems to be incorrect based on the calculations. The correct answer should be (c) 6 km.
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Community Answer
A train starting from rest attains a velocity of 72 km/h in 5 minutes....
u = 0, v = 72 km/h = 72 × (5/18)= 20 ms–1,
t = 5 minutes=300s
a =(v-u)/t =20/300=1/15 m/s2
=>v2=u2+2as=3000ssms=3kms.
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