Question

A train starts from rest at s = 0 and is subjected to
acceleration as shown:
a(m/s)
30 s (m)
(A) change in velocity at the end of 10 m
displacement is 50 m/s
(B) velocity of the train for s = 10 m is 10 m/s
(C) the maximum velocity attained by train is not
greater than 14 m/s
(D) the maximum velocity of the train is between 15
m/s and 16 m/s
​

Answer 1

A change in velocity

Answer 2

Answer:

The velocity of the train at displacement $s=10$ $m$ is $10$ $m/s$. The maximum velocity that the train attains is not greater than $14$ $m/s$. (B) and (C) are correct options.

Explanation:

We will first calculate the velocity of the train at displacement $s=10$ $m$.

The area of the graph at displacement $s=10$ $m$ is:

$Area=\frac{1}{2} \times 10 \times (6 +4)=\frac{v^{2} }{2}$

where $v$ is the velocity of the train at displacement $s=10$ $m$

$v=10$ $m/s$

So, the velocity of the train at displacement $s=10$ $m$ is $10$ $m/s$.

Also, the area of the graph at displacement $s=30$ $m$ is:

$Area=\frac{1}{2} \times 30 \times 6=\frac{Vmax^{2} }{2}$

$Vmax^{2} =180$

$Vmax=13.41$ $m/s$

So, the maximum velocity that the train attains is not greater than $14$ $m/s$

Hence, (B) and (C) are correct options.