Atrain accelerates from rest with as = 1.2 m, for 10 s. after that it moves at constant speed for another 15 s. find the total distance covered by the train during the total 25 s.

The total distance covered during the 25 s is 240 m

Explanation:

Hi there!

The position and velocity of the train can be calculated using the following equations:

x = x0 + v0 · t + 1/2 · a · t²

v = v0 + a · t

Where:

x = position at time t

x0 = initial position

v0 = initial velocity

t = time

a = acceleration

v = velocity at time t

When the velocity is constant the position equation is reduced to this expression:

x = x0 + v · t   Where "v" is the velocity.

First, let´s calculate the distance traveled during the first 10 s:

x = x0 + v0 · t + 1/2 · a · t²

x = 0 m + 0 m/s · 10 s + 1/2 · 1.2 m/s² · (10 s)²

x = 60 m

The velocity reached after 10 s of acceleration will be:

v = v0 + a · t

v = 0 + 1.2 m/s² · 10 s

v = 12 m/s

Now, we can calculate the distance covered during the next 15 s at constant speed:

x = x0 + v · t

x = 60 m + 12 m/s · 15 s

x = 240 m

The total distance covered during the 25 s is 240 m

Have a nice day!

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