Answer to Question #105310 in Mechanics | Relativity for Sridhar

Question

The speed of a particle changes from √5m/s to 2√5m/s in a time 't' . If the magnitude of change in its velocity is 5m/s the angle between the initial and final velocities of the particle is
Ans:90°

Answer 1

Initial speed$=\sqrt{5} m/sec$

Final speed $=2\sqrt{5} m/sec$

And magnitude of change in velocity is $5m/sec$ which is equal to $\sqrt{(\sqrt{5})^2+({2\sqrt{5}})^2}$ which means that magnitude in change of velocity is the unique case with velocities at different states do not have components in a common direction.

For example,Initial velocity$=\sqrt{5}\hat {i}$

Final velocity$=2\sqrt{5} \hat{j}$

Magnitude of change in velocity$=|2\sqrt{5}\hat{j}-\sqrt{5}\hat{i}|=\sqrt{(\sqrt{5})^2+({2\sqrt{5}})^2}=5m/sec$

Dot product of initial and final velocities$=(\sqrt{5}\hat{i}).(2\sqrt{5}\hat{j})=0$

or we can say the velocity at different states are perpendicular to each other or angle between them is $90\degree.$