Question

An object moves in a straight line. Its instantaneous velocity is in negative and its instantaneous acceleration is positive. Which of the following can be determined about the object's motion-
(A) The object is speeding up
(B) The object will come to rest
(C) The object is slowing down
(D) The object will change direction
(Please mention the answer with proper reason)​

Answer 1

Answer:

B is the correct one 0bbbb

Answer 2

Answer:

when instantaneous velocity is negative and its instantaneous acceleration is positive, then the object is slowing down

Explanation:

Instantaneous velocity:

• Instantaneous velocity is a continuous function of time.
• It defines the velocity of an object at any point in time during its motion.
• It is given by the time derivative of the position function

        $v(t)=\dfrac{dx(t)}{dt}$

• It is a vector quantity, can be positive or negative.
• Slope of position-versus-time graph at a particular time gives instantaneous velocity at that time.
• Similarly the the time derivative of the velocity defines the instantaneous acceleration.

       $a(t)=\dfrac{dv(t)}{dt}=\dfrac{d^{2} x(t)}{dt^{2} }$

• If the object is speeding up or moving in a positive direction, then it has a positive velocity. Thus, the acceleration is in the same direction, hence the acceleration is positive.
• When the object is slowing down or moving in the negative direction, then it has a negative velocity. Thus, the acceleration is in the opposite direction of the velocity and hence the object has a positive acceleration.

Thus, when instantaneous velocity is negative and its instantaneous acceleration is positive, then the object is slowing down.

So, the correct answer is option C.

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