Question

A certain particle undergoes erratic motion. At every point in its motion, the direction of the particle's momentum is always
a) the same as the direction of its velocity
b) the same as the direction of its acceleration
c) the same as the direction of its net force
d) the same as the direction of its kinetic energy

Answer 1

Momentum of a body is defined as the product of its mass and velocity. It is a vector quantity having both magnitude and direction. So, we can use this formula to identify the direction of momentum: $\overset{\to }{\mathop{p}}\,=m.\overset{\to }{\mathop{v}}\,$

Complete step by step answer:
As we know , momentum is given as: $\overset{\to }{\mathop{p}}\,=m.\overset{\to }{\mathop{v}}\,$, where $\overset{\to }{\mathop{p}}\,$ is a vector quantity having magnitude as well as direction. Also, we have mass m as a scalar quantity. Therefore, we are left with a velocity of $\overset{\to }{\mathop{v}}\,$ to decide for the direction of momentum. Since $\overset{\to }{\mathop{v}}\,$is also a vector quantity having magnitude as well as direction. So, at every point of its motion, the direction of a particle’s momentum is always in the same direction as the direction of its velocity.
Hence,option(a) is the correct answer.

Note: The momentum of a body depends on the frame of reference. Momentum is always conserved in inertial frames of reference. Total mechanical energy is conserved only inelastic collisions whereas momentum is conserved both in elastic and inelastic collisions.There are two types of momentum, linear momentum, and angular
momentum.Photons are massless but they have momentum. Their momentum is defined as the ratio of their energy and the speed of light in a vacuum.