# Calculation of distance and displacement

The area covered between the velocityâ€“time graph and time axis gives the displacement and distance traveled by the body for a given time interval.

Total distance = |

*A*_{1 }| + |*A*_{2 }| + |*A*_{3 }|= Addition of modulus of different area,

i.e.,

Total displacement =

*A*_{1}+*A*_{2}+*A*_{3}= Addition of different area considering their sign

i.e.,

The area above time axis is taken as positive, while the area below time axis is taken as negative.

Here,

*A*_{1}and*A*_{2}are the area of triangles 1 and 2, respectively, and*A*_{3}is the area of trapezium (Figure).# Calculation of acceleration

The slope of tangent on velocityâ€“time graph represents the acceleration of the particle.

During the motion from O â†’

*A*, acceleration is positive.During the motion from A â†’

*B*, acceleration is negative.During the motion from B â†’

*C*, acceleration is positive.During the motion from C â†’

*D*, acceleration is zero.During the motion from D â†’

*E*, acceleration is negative.# Graph

*v*= constant, i.e., line parallel to time axis represents that the particle is moving with constant velocity.

Slope is infinite hence acceleration is infinite, i.e., line perpendicular to time axis represents that the particle is increasing its velocity, but time does not change. It means the particle possesses infinite acceleration.

*Practically, it is not possible.*

Slope is constant and positive hence acceleration is constant and

*v*is increasing uniformly with time, i.e., line with constant slope represents uniform acceleration of the particle.Slope is increasing, the acceleration is not constant. Acceleration is increasing.

Slope is decreasing, the acceleration is not constant. Acceleration is decreasing.

Slope is positive but constant. Hence, acceleration will be positive and constant.

Slope is negative but constant. Hence, acceleration will be negative and constant.

# Some Important Notes

- For two particles having displacement time graph with slopes
*Î¸*_{1}and*Î¸*_{2}^{ }and possessing velocities*v*_{1}and*v*_{2 }, respectively, . - Greater the slope of displacement-time graph, greater is the velocity and vice-versa.
- Area under
*vâ€“t*graph = displacement of the particle.