Single Choice

In one dimensional motion, instantaneous speed $$v$$ satisfies the condition, $$ 0 \leq v < v_0$$,when

AThe displacement in time T must always take non-negative values.
BThe displacement x in time T satisfies - $$v_0T < x < v_0T$$.
Correct Answer
CThe acceleration is always a non-negative number.
DThe motion has no turning points.

Solution

By definition, instantaneous velocity, $$v=\dfrac{dx}{dt}$$

where, $$x=$$ displacement, $$T=$$ time

$$\implies dx=v.dt$$

$$\implies x(0)=v_0(T-0)$$

$$\implies x=v_oT$$

If the velocity is positive or towards the right of origin,
Then $$x=+ v_0T$$, maximum displacement $$=+v_0T$$

But if the velocity is negative or towards left of origin
Then $$x=-v_0T$$, maximum displacement $$=-vT$$

Hence, the displacement $$x$$ in time $$T$$ satisfies $$-v_0T

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