Grade 11Mechanics
An object moves with a constant acceleration ![src=data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAABUAAAAXCAIAAABrvZPKAAAAiElEQVQ4jeWTwRHAIAgEqYuCqOeqoRmKSR5qIhEdHfPJ5N4sd8BAx57oY7yBGbblb2ASDXgVmlfu8Kb/JLw7v1OHN3AZlGEqd+AJXiVhVSeXecin+spOZYA3vIF9uYGpm77hV/Enr+LDN/2W+HyFgf0ovwoDZXnRCVWIOvu/bMtPRBlCflF/509Zzf6jTiBBCAAAAABJRU5ErkJggg==]()
. Which of the following expressions are also constant?
1 Answer
Aditi Chauhan
We assume that the object starts its motion from rest.
The velocity vector at any time t is given as:
(A) will be the correct option.
If the acceleration of an object is constant, the acceleration vector
must always point in same direction and have the same magnitude.The acceleration vector of the object can be mathematically defined as:
Therefore the magnitude of the acceleration vector is:
Therefore (B) is the correct option.
It is clear that this term is dependent on time t and is not constant. Therefore, (C) is not the correct option.
One should note that even if the initial velocity vector of the object is zero, the term
![\frac{d}{dt}[v^{2}]](https://files.askiitians.com/cdn1/cms-content/common/latex.codecogs.comgif.latex_fracddtv2.jpg)
would be dependent on variable t.The vector
is the unit vector, and therefore has a magnitude equal to 1. Differentiation the magnitude of vector will give zero and is a constant value.Therefore (D) is the correct option.
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