#### IIT (NTSE/Olympiad)

# Motion in one Dimension

__Comparative Study Of Average Speed & Average Velocity__

__Comparative Study Of Average Speed & Average Velocity__

The average speed of a particle for a given interval of time is defined as the ratio of distance travelled to the time taken, while average velocity is defined as the ratio of displacement to time taken.

Average speed =

i.e. v

Average velocity =

i.e Note :(a) Average speed is a scalar, while average velocity is a vector both having same unit (m/s)

(b) Both have dimension [M

(c) For a given time interval average velocity is single valued, while average speed can have many values depending on path followed.

(d) If after motion body comes back to its initial position = 0 [as &Delta = 0], but v

(e) For a moving body average speed can never be negative or zero (unless t → ∞), while average velocity can be i.e.

V

(f) In general average speed is not equal to magnitude of average velocity (as Δ s ≠ | Δ |). However it can be so if the motion is along a straight line without change in direction (as Δ s = | Δ |).

(g) If a graph is plotted between distance (or displacement) and time, the slope of chord during a given time interval gives average speed (or velocity)

Average speed =

i.e. v

_{av}=Average velocity =

i.e Note :(a) Average speed is a scalar, while average velocity is a vector both having same unit (m/s)

(b) Both have dimension [M

^{0}LT^{–1}](c) For a given time interval average velocity is single valued, while average speed can have many values depending on path followed.

(d) If after motion body comes back to its initial position = 0 [as &Delta = 0], but v

_{av}> 0 and finite (as Δ s > 0)(e) For a moving body average speed can never be negative or zero (unless t → ∞), while average velocity can be i.e.

V

_{av}> 0 while > = or < 0(f) In general average speed is not equal to magnitude of average velocity (as Δ s ≠ | Δ |). However it can be so if the motion is along a straight line without change in direction (as Δ s = | Δ |).

(g) If a graph is plotted between distance (or displacement) and time, the slope of chord during a given time interval gives average speed (or velocity)

#### IIT (Class X)

- Unit, Dimension & Error

- Vectors

- Motion in One Dimension
- Distance
- Displacement
- Comperative Study of Distance & Displacement
- Speed
- Velocity
- Comparative Study of Instantaneous Speed and Instantaneous Velocity
- Comparative Study Of Average Speed & Average Velocity
- Acceleration
- Motion With Uniform Acceleration
- Motion Under Gravity
- Relative – Velocity
- Points to Remember - Motion in One Dimension

- PROJECTILE MOTION

- NEWTON'S LAWS OF MOTION & FRICTION

- WORK, POWER, ENERGY & CONSERVATION LAWS

- CIRCULAR MOTION & ROTATIONAL DYNAMICS

- GRAVITATION