A three-wheeler starts from rest, accelerates uniformly with $1 \mathrm{m} {\mathrm{s}}^{-2}$ on a straight road for $10 \mathrm{s}$, and then moves with uniform velocity. Plot the distance covered by the vehicle during the $\mathrm{n}$ th second $(\mathrm{n}=\mathrm{1,2},3\dots .)$ versus $\mathrm{n}$. What do you expect this plot to be during accelerated motion: a straight line or a parabola?

1. Average speed:

It is the ratio of the total distance to the total time.

2. Average Velocity:

It is the ratio of the total displacement to the total time.

3. Instantaneous Velocity:

(i) It is the rate of displacement with respect to time

(ii) Mathematically expressed as, $\overrightarrow{v}= \underset{\text{Δ}\text{t}\to 0}{\lim }\frac{\text{Δ}\overrightarrow{x}}{\text{Δ}\text{t}}= \frac{\mathrm{d}\overrightarrow{x}}{\mathrm{d}t}$

4. Average acceleration:

It is the ratio of total change in velocity to the total time taken.

5. Instantaneous Acceleration:

(i) It is the rate of change of velocity

(ii) Mathematically, it is expressed as, $\overrightarrow{a}= \underset{\text{Δ}\text{t}\to 0}{\lim }\frac{\text{Δ}\overrightarrow{v}}{\text{Δ}\text{t}}= \frac{\mathrm{d}\overrightarrow{v}}{\mathrm{d}t}$

6. Motion from a graph:

(i) The slope of distance-time graph gives speed.

(ii) The slope of displacement-time graph gives velocity.

(iii) The slope of velocity-time graph gives acceleration.

(iv) The area under velocity-time graph gives displacement.

(v) The area under speed-time graph gives distance.

(vi) The area under acceleration time gives change in velocity.

7. Equations of Motion (for constant acceleration):

(i) $v= u+at$

(ii) $s= ut+\frac{1}{2}a{t}^2$

(iii) $v^2= u^2+2as$

(iv) $s= \frac{\left(u+v\right)}{2}t$

(v) $s_n= u+\frac{a}{2}(2n-1)$

8. Relative motion:

(i) ${\overrightarrow{v}}_{AB}$ (velocity of A with respect to B) $= {\overrightarrow{v}}_A-{\overrightarrow{v}}_B$

(ii) ${\overrightarrow{a}}_{AB}$ (acceleration of A with respect to B) $= {\overrightarrow{a}}_A-{\overrightarrow{a}}_B$