Question

Impulse is
$A.$ a scalar quantity
$B.$ a vector quantity
$C.$ neither a scalar quantity
$D.$ sometimes a scalar and sometimes a vector

Answer 1

Hint: Here we will proceed by defining the impulse with the help of a derivation to find out whether impulse a scalar quantity or vector quantity.

Complete step-by-step answer:

Momentum – Momentum is a measure of strength and a measure of how hard it is to stop an object. An object which is not moving has a zero momentum.

Scalars versus Vector:

There are two types of quantities in physics, vectors and scalars. The quantities that have both magnitude and direction are called vectors. Scalars are quantities that only have magnitude.

Impulse is defined as,

It is defined as the product of net force and the length of time it was applied.
$\vec J = {\vec F_{net}}dt$
Since net force is given by the change in momentum with respect to time $\left( {{{\vec F}_{net}} = \dfrac{{d\vec p}}{{dt}}} \right)$ the equation becomes
$\vec J = \dfrac{{d\vec p}}{{dt}}dt$

Cancelling out the time variable, leaving us with the second, more simple, definition of impulse; it is the change in momentum

$\vec J = \vartriangle \vec p$

As we know that momentum and force are both vectors, therefore impulse is also a vector.
Force, momentum and impulse all have the same direction. Momentum is a vector since it is the product of velocity and mass, because scalar times a vector is always a vector.
Net force remains constant, so impulse is a

Linear function of time, so ${\vec F_{net}} = \dfrac{{d\vec p}}{{dt}} = \dfrac{{\vartriangle \vec p}}{{\vartriangle t}}$

(where J , p, t are impulse,momentum and time respectively)
We know that,

$\operatorname{Im}pulse = force \times time$

Force is a vector quantity because it has both magnitude and direction and time is a scalar quantity. The product of vector and scalar is always vector, so impulse is a vector quantity with S.I. unit kilogram meter per second.

In a nutshell, we can say that Impulse is a vector quantity as it has both magnitude as well as direction. Mathematically, impulse is equal to the change of momentum of the body.
$\therefore \vec I = {\vec P_{final}} - {\vec P_{initial}}$.

Therefore, B is the correct option.

Note – Whenever we come up with this type of question, one must know that impulse (symbol by J or imp) is the integral of a force, over the time interval, t, for which it acts. The S.I. The unit of impulse is the Newton second. By using this concept, we can solve the questions related to impulse.