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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.

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 t

_{B}. 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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