What would you call the area under the curve of a velocity-time graph included between itself and two time ordinates?

CONCEPT:

• Displacement (X): The change in the position of an object is called displacement.
  • Displacement is a one-dimensional quantity representing the smallest separation between two defined points.
  • The standard unit of displacement in the International System of Units (SI) is the meter (m).

• Velocity (V): The rate of change of displacement is called velocity. It is a vector quantity. 

  • The SI unit of velocity is called m/s and the CGS unit is cm/s.

  • The slope of the displacement-time graph gives the velocity.

\(Instantaneous\;velocity\;\left( V \right) = \frac{{dx}}{{dt}}\)

\(V = \frac{{dx}}{{dt}}\)

Hence dx = V dt 

\(Displacement\;\left( X \right) = \mathop \smallint \nolimits_{{x_1}}^{{x_2}} dx = \mathop \smallint \nolimits_{{t_1}}^{{t_2}} V\;dt\)

• Thus the area under the velocity-time graph gives the displacement. Similarly, the area under-speed time graph gives the total distance travelled.

EXPLANATION:

• The area under a velocity-time graph is a representation of the displacement. So option 2 is correct.
• The rate of change of distance is called speed.
• The rate of change in velocity is called acceleration.