**Velocity-time graph**

**Velocity-time graph**

With respect to velocity-time plot, the following points have to be kept in mind to extract maximum information.

Velocity and speed of particle at any instant can be found easily from velocity-time plot

the time interval is equal to the area under velocity time graph. From the velocity-time graph, we can also find the distance travelled, the only point you have to keep in mind is whether the velocity is changing its sign or not. If velocity is not changing its sign in a particular time-interval, the distance = displacement= area under v-t curve, but if velocity is changing its sign, then displacement = area under v-t curve and displacement = sum of the area of v-t curve below and above the time axis

- We can also find average speed and average velocity for the anytime interval from the v-t plot.

As acceleration

so the slope of the tangent drawn to velocity-time plot gives acceleration. If the v-t plot is a straight line, the acceleration is constant.

- The instant (time) where the velocity-time plot is crossing time axis, is the moment when the particle is changing its direction of motion.
- While drawing x-t plot from the velocity-time plot, be careful about the initial velocity.
- Illustration An application illustrating the concepts related to the velocity-time graph of a particle moving along a straight line whose velocity varies with time as shown in gure.

- The velocity of the particle for 0 < t < t 1 is positive and increasing with constant acceleration as the v-t curve is a straight line. For this interval acceleration is +ve.

t _{1} < t < t _{2} is positive and constant and acceleration is zero.

t _{2} < t < t _{3} is positive and decreasing with varying acceleration along -ve x-direction. Hereafter seeing the curve we can say that value of

is decreasing i.e. acceleration is -ve whose magnitude is decreasing with time. t = t _{3} is zero and this is the instant where the particle is changing its direction of motion. t 3 < t < t 4 is negative and increasing in opposite direction while the description of acceleration would be the same as that for t _{2} < t < t _{3}. t = t _{4} is negative and acceleration changes its direction

t 4 < t < t 5 is ve and decreasing in magnitude as acceleration is positive, whose magnitude is increasing.

- For 0 < t < t 3 , Distance = Displacement = Area under velocity-time graph. For t > t 3 measured from t = 0, distance and displacement won’t be equal. For e.e., the displacement in 0 to t 5 is [Area of OABCD Area of DEF] while distance is [Area of OABCD Area of DEF].
- The rough distance-time plots and displacement-time plots drawn:

Here, we have assumed that the Area of OABCD > Area of DEF Note carefully the slope of the drawn plot at t = 0.

- A rough acceleration-time plot for a given velocity-time plot can be drawn as

The exact variation of acceleration for t _{2} - t _{4} and from t _{4} – t _{5} can’t be known from velocity-time plot unless we know the equation for the v-t plot, that’s why we have drawn all three possibilities.