The velocity is positive when there is a displacement of the object from its initial position and it can be determined by how much is the displacement of the object in a given time interval.

**The acceleration of the object is positive if the velocity of the object increases with time, likewise, the acceleration is negative if the velocity decreases with time. This is seen in the case of objects coming to its static state of equilibrium or rest. This article deals with the negative acceleration positive velocity.**

**What is meant by Positive Velocity?**

The velocity of the object is determined by the time required for its displacement.

**The velocity is positive if the change in the position of the object is positive and it is calculated using the formula:-**

V=X_{2}-x_{1}/t_{2}-t_{1}

Time is an irreversible quantity and hence the change in time is always positive, whereas the velocity is positive if the change in displacement of the object x_2-x_1 x_{2}-x_{1}is positive. If the displacement is reversed and thus x_2-x_1 x_{2}-x_{1}becomes negative then the velocity is found to be negative.

**What is Negative Acceleration?**

The acceleration in simple words is a change in the speed of the object in the variable of time.

**If the speed of the object decreases with time then the difference in speed will be negative. The acceleration is the change in speed with respect to time and is given by the formula **

If the change in the final and initial velocity of the object v_{2}-v_{1} is negative that is v_{2}-v_{1} then the acceleration will be negative. And if the velocity increases with time we will have a positive acceleration since v_{2}>v_{1}. If the velocity does not change with time that is final and the initial velocity remains the constant v_{2}=v_{1}, the object is not accelerating, the acceleration is zero.

**How can Acceleration be Negative when Velocity is Positive?**

The velocity of the object is positive if there is a displacement of the object.

**If the velocity of the object decreases with time then the rate of change of velocity will be negative and hence the acceleration is negative.**

The reduction of the velocity of the object is seen in the case of the object slowing down or coming to the static position of rest.

**Example: Consider a car moving at a speed of 60km/h on the main road. After a drive of half an hour, the car passes the village and reduces its speed to 20km/h. What is the acceleration of a car?**

**Given:** The initial speed of the car v_{1}=60km/h

The final speed of the car v_{2}=20km/h

The time taken is t= 0.5 hr =-40/.5

Hence the acceleration is

a=v_{2}-v_{1}/t_{2}-t_{1}

=20-60/.5

The acceleration of the car is **-80 km/h**.

**Velocity v/s Time Graph for Negative Acceleration**

Let us plot a graph of velocity v/s time to know how we find negative acceleration.

It is clear that the slope of the velocity and time graph gives us the acceleration. Since the velocity of the object decreases with time, the rate of change of velocity will be negative and hence we have negative acceleration.

**How can we have Negative Acceleration if the Object is moving in the Reverse Direction?**

If the object is moving in the reverse direction then the velocity of the object is evidently negative.

**For acceleration now to be negative the negative velocity of the object has to be decreased further such that the change in the final and initial velocity still remains negative with respect to time.**

This is seen if the velocity of the object increases in the reverse direction and since the mobility of the object is in the reverse direction the velocities are taken as negative. This is also the case if the object continues to de-accelerate further.

**Example: Suppose the object is moving in the reverse direction with an initial velocity of 10 m/s and then accelerates and change the speed to 18m/s in 25 seconds then what is the acceleration of the object?**

**Given:** The acceleration of the object is in the reverse direction and hence the change in the position of the object is negative and hence the velocity.

Therefore, the initial velocity of the object is v_{1}=-10m/s V_{1}=-10m/s v1=-10m/s

The final velocity of the object is v_{2}= V_{2}=-18m/sv2=

The time interval t= 25 seconds

Hence, the acceleration of the object is

A=v_{2=}v_{1}/t_{2}-t_{1}

=-18-(-10)/25

=-18+10/25

=-8/25

=0.32m/s

The acceleration of the object is found to be **-0.32 m/s**.

**Frequently Asked Questions**

**What is the acceleration of a bicycle if the speed of the bicycle reduces at the rate of 3 m/s every 30 seconds?**

The velocity of the bicycle reduces frequently after every half a minute, hence the change in the velocity is -3m/s.

We have,

The acceleration of the bicycle is **-0.1m/s ^{2}**.

**Does the velocity of the object be negative?**

The velocity if the change in the displacement of the object with time and is given by V=x_{2}-x_{1}/t_{2}-t_{1}

**If x _{2}>x_{1}then the change in the displacement with respect to time will be negative and hence the velocity is negative. This is the case when the object moves in the reverse direction.**

**What is centripetal acceleration?**

The centripetal force keeps the object in a circular motion.

**The centripetal acceleration is the variation in the velocity of the object in the centripetal motion.**

**What are some examples of negative acceleration?**

The negative acceleration is seen in the case of objects de-accelerating to reach back to the static state.

**Some examples of negative acceleration are a car climbing up the hill, a ball slowing down after a kick, the flow of water after a waterfall, propellers of fans turned OFF, the speed of an athlete after crossing the finish line, etc.**

**What is meant by the de-acceleration of the object?**

The de-acceleration of the object implies the reduction of the velocity with elapsing distance.

**If the velocity of the object keeps on decreasing continuously, then the rate of change in the velocity will be negative and hence the acceleration is negative, hence de-acceleration signifies the negative acceleration of the object.**