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# Speed vs Time Graphs

Speed is the ratio of distance to time. It is measures in m/s or km/h or mi/h. the difference between speed and velocity is that speed is a scalar quantity and velocity is a vector quantity.

Speed vs time graph is the graph made by marking speed on y coordinate axis and time on x coordinate axis.

The slope of the velocity time graph gives us the acceleration, since acceleration is the rate of change of speed with respect to time. It is calculated in m/s$^{2}$ or km/h$^{2}$ etc.

The shape of the velocity time graph for either constant velocity or changing velocity reveals the fact about the acceleration of the object or person. Slope is equal to zero implies acceleration is zero, slope is positive implies acceleration is positive and slope is negative implies acceleration is negative.

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## Constant Velocity Graph

Following graph represents, constant velocity graph: Constant Velocity Graph (Zero Acceleration)

This implies that when the velocity is constant then we get a line on the graph parallel to x axis depicting constant velocity.

In this case since change in velocity is equal to zero, therefore, acceleration is also equal to zero.

We denote acceleration by ‘a’. In all the formulas based on acceleration ‘a’ we can substitute a = 0 in cases of constant velocity.

## Positive Velocity at Given Instant

When the velocity increases with time we get a positive acceleration. When the velocity is changing we can only determine acceleration at any instant and not on whole graph and it is obvious that acceleration can be determine by the slope of the curve at an instant: Positive Velocity at Given Instant (Positive Acceleration)

The picture above displays positive velocity and positive acceleration.

In order to obtain the acceleration on the whole graph we need to find the average of all accelerations determine at given time periods.

## Negative Velocity at Given Instant

When the velocity increases or decreases in negative region with time we get a negative acceleration. Negative Velocity at Given Instant (Negative Acceleration):

The picture above displays negative velocity and negative acceleration.

## Steps & Method

Steps & Method of Solving Based on Zero/Positive/Negative Acceleration:

There are two parts to be understood.
The first one is calculating average acceleration. We follow the following steps to obtain the same:

1) First step is to understand the acceleration with the sign positive or negative whichever is applicable.

2) Use the formula:

$Acceleration$ = $\frac{(change\ in\ velocity\ from\ start\ to\ end)}{(change\ in\ time\ from\ start\ to\ end)}$

3) Determine the change in velocity that is difference of initial and final velocity and note it.

4) Determine the change in time that is difference of initial and final time and note it. Here it is clear that initial time will be equal to zero always           until and unless problem says about it.

5) Now substitute the values from step 4 and 5 in the formula mentioned in step 2 and obtain the result.
The second method is understanding of positive and negative acceleration. We follow the steps below.

1) Understanding clearly the direction of the acceleration. For example moving in one direction in the line of velocity means positive acceleration and movement in other direction of the line of velocity implies negative acceleration.

2) The definition of acceleration can be used as well to determine positive or negative acceleration which is given by difference of final velocity and initial velocity.

3) It is important to understand the speeding up in every direction. In this case we will have positive acceleration.

4) Also understand the slowing down in all directions. In this case we will have negative acceleration.
While speed is a scalar quantity, both velocity and acceleration are vector quantities so it is very important to take in consideration the directions associated with them respectively. Also acceleration is obtained by the slope of the velocity time graph and tells us whether the object has zero acceleration, positive acceleration or negative acceleration.

Also the difference of positive and negative velocity is important to understand to be accurate in calculations. We have seen that we get positive velocity when line is lying in positive region of the graph which is above the x axis and we get negative velocity when the line of the graph is lying in the negative region of the graph that is the region below the x axis. In all cases, the sign is significant for telling the direction of velocity and acceleration.

We might have cases with crossed over line of the graph from positive region to negative region or so. In this case we say that the object or person has changed directions.

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