Question

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

Answer 1

The total distance covered during the 25 s is 240 m

Step-by-step 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!