Question

In one dimension motion,
instantaneous speed v
satisfies 0 $\le v<v_0.$

• A. The motion has no turning points
• 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 displacement in time T must
  always take non – negative values

Answer 1

The correct option is B The displacement x in time

T satisfies - $v_{0}T$ < x < $v_{0}T$

Answer) Instantaneous velocity, $v=\frac{dx}{dt}$
x= displacement, t = time

${\int }_0^x\text{dx}={\int }_0^T{v}_0.dt$

x= $v_0$ (T-0)
x= $v_{0}T$

The velocity is towards positive x direction,

Maximum displacement = + $v_{0}T$

The velocity is towards negative x direction,

Maximum displacement = - $v_{0}T$

Final answer : B