# Q.46. The graph shows position as a function of time for two trains A and B running on parallel tracks. For time t > 0, which of the following statements is true ? (A) At time ${t}_{B}$ both trains have the same velocity. (B) Both trains speed up all the time. (C) Both trains may have the same velocity at some time earlier than ${t}_{B}$. (D) Graph indicates that both trains have the same acceleration at a given time.

Dear Student

Correct option is c.
Option a is wrong because at time B, the displacements are identical, but the slopes are not, so the velocities are different.
The slope of A has a constant value, while the slope of B is greater at the initial point and less at  tB.  So A is not speeding hence option B is wrong.

The slope of B must change continuously from the first value to the latter, so at some intermediate time, it must equal the slope of B. So correct option is c.

As A has constant slope so acceleration is zero for it hence option d is also wrong.

Regards

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