Question

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

• 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.

Answer 1

The correct option is B The displacement x in time T satisfies - $v_{0}T<x<v_{0}T$.

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

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

$⟹dx=v.dt$

$⟹x\left(0\right)=v_0(T-0)$

$⟹x=v_{o}T$

If the velocity is positive or towards the right of origin,

Then $x=+v_{0}T$, maximum displacement $=+v_{0}T$

But if the velocity is negative or towards left of origin

Then $x=-v_{0}T$, maximum displacement $=-vT$

Hence, the displacement $x$ in time $T$ satisfies $-v_{0}T<x<v_{0}T$