First slide

Position Path Length (Distance) And Displacement

Question

In one dimensional motion, instantaneous speed v satisfies $0 \leq v < v_{0}$ . Then, which of the following statement is true?

Moderate

A

The displacement in time T must always take non-negative values.
B

The displacement x in time T satisfies $- v_{0} T < x < v_{0} T$ .
C

The acceleration is always a non-negative number.
D

The motion has no turning points.

Solution

For maximum and minimum displacement, we have to keep in mind the magnitude and direction of maximum velocity.
As maximum velocity in positive direction is v₀ maximum velocity in opposite direction is also v₀.
Maximum displacement in one direction = v₀T
Maximum displacement in opposite directions $= - v_{0} T$
Hence, $- v_{0} T < x < v_{0} T .$

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