The following are four different relations about displacement, velocity, and acceleration for the motion of a particle in general.
(a) | \(v_{avg}=\frac{1}{2} [ v(t_{1})+v(t_{2}) ]\) |
(b) | \(v_{avg}=\frac{r(t_{2})-r(t_{1})}{t_{2}-t_{1}}\) |
(c) | \(r=\frac{1}{2}[ v(t_{2})-v(t_{1}) ](t_2-t_1)\) |
(d) | \(a_{avg}=\frac{v(t_{2})-v(t_{1})}{t_{2}-t_{1}}\) |
Assertion (A): | For a given initial and final position the average velocity is single-valued while the average speed can have many values. |
Reason (R): | Velocity is a vector quantity and speed is a scalar quantity. |
1. | Both (A) and (R) are True and (R) is the correct explanation of (A). |
2. | Both (A) and (R) are True but (R) is not the correct explanation of (A). |
3. | (A) is True but (R) is False. |
4. | Both (A) and (R) are False. |