An object travels North at # 4 m/s# for #1 s# and then travels South at # 5 m/s# for # 7 s#. What are the object's average speed and velocity?

Answer 1

#V_(avg)=-3.875m/s#

#S_(avg)=4.875m/s#

Since the average velocity is a vector quantity, the velocities' signs are taken into account.

Initially, ascertain the two velocities:

Although you are free to define your system however you see fit, I will here define North as the positive direction and South as the negative direction.

North at #4m/s# is #4m/s#
South at #5m/s# is #-5m/s#

Then, you take the mean of these two measurements, adding time to the equation.

#V_(avg)="displacement"/(Deltat)=(v_1t_1+v_2t_2)/(Deltat)#
#V_(avg)=(4m/s*1s-5m/s*7s)/(8s)=-3.875m/s#
A good way to understand this is to think about how averages are taken. You add up the total amount of all the items, then divide by the number of items. This is the same principle here: we are adding up all the 1 second intervals of velocity then dividing by the total number of 1 second intervals. You can also think of it as measuring the displacement (#v*t#) and dividing by the time it took to get there.

Considering that the average speed is a scalar quantity, the signs of the velocities are ignored.

The easiest method to find average speed is to calculate the total distance traveled. In this problem, average speed can be found using the following equation because there are only two possible directions of travel: up or down.

#S_(avg)="distance"/(Deltat)=(abs(v_1t_1)+abs(v_2t_2))/(Deltat)#
#S_(avg)=(abs(4m/s*1s)+abs(-5m/s*7s))/(8s)=4.875m/s#
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Answer 2

Average speed: (3.14 , \text{m/s}), Average velocity: (0.43 , \text{m/s} , \text{South})

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Answer from HIX Tutor

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

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