First, let's consider the first part of the journey where the train accelerates from rest at a constant rate 𝛼 for distance x1 and time t1.

Using the equation of motion:
s = ut + 0.5at^2
where:
s = distance
u = initial velocity
a = acceleration
t = time

Since the train starts from rest, u = 0. So, the equation becomes:
x1 = 0.5*𝛼*t1^2

Next, let's consider the second part of the journey where the train retards to rest at constant rate 𝛽 for distance x2 and time t2.

Again using the equation of motion, and since the train finally comes to rest, the equation becomes:
x2 = 0.5*𝛽*t2^2

Now, let's divide the first equation by the second equation:

(x1/x2) = (0.5*𝛼*t1^2) / (0.5*𝛽*t2^2)
= (x1/x2) = (𝛼/𝛽) * (t1/t2)^2

So, the correct relation is not given in the options A, B, C, or D. The correct relation should be (x1/x2) = (𝛼/𝛽) * (t1/t2)^2.

Question

First, let's consider the first part of the journey where the train accelerates from rest at a constant rate 𝛼 for distance x1 and time t1.

Using the equation of motion: 
s = ut + 0.5at^2
where:
s = distance
u = initial velocity
a = acceleration
t = time

Since the train starts from rest, u = 0. So, the equation becomes:
x1 = 0.5*𝛼*t1^2

Next, let's consider the second part of the journey where the train retards to rest at constant rate 𝛽 for distance x2 and time t2.

Again using the equation of motion, and since the train finally comes to rest, the equation becomes:
x2 = 0.5*𝛽*t2^2

Now, let's divide the first equation by the second equation:

(x1/x2) = (0.5*𝛼*t1^2) / (0.5*𝛽*t2^2)
=> (x1/x2) = (𝛼/𝛽) * (t1/t2)^2

So, the correct relation is not given in the options A, B, C, or D. The correct relation should be (x1/x2) = (𝛼/𝛽) * (t1/t2)^2.

Knowee AI · Accepted Answer