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An object moves with a constant acceleration . Which of the following expressions are also constant?

An object moves with a constant acceleration . Which of the following expressions are also constant?

Grade:11

1 Answers

Aditi Chauhan
askIITians Faculty 396 Points
9 years ago
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We assume that the object starts its motion from rest.
The velocity vector at any time t is given as:

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(A) will be the correct option.
If the acceleration of an object is constant, the acceleration vector \overrightarrow{a}must always point in same direction and have the same magnitude.
The acceleration vector of the object can be mathematically defined as:
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Therefore the magnitude of the acceleration vector is:
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Therefore (B) is the correct option.
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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}] would be dependent on variable t.
The vector \frac{\overrightarrow{v}}{\overrightarrow{|v|}}is the unit vector, and therefore has a magnitude equal to 1. Differentiation the magnitude of vector \frac{\overrightarrow{v}}{\overrightarrow{|v|}}will give zero and is a constant value.
Therefore (D) is the correct option.


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