Eb3 Velocity and Time: Calculate $V_{av}, v_{av}$, and Time to Fly $3.5 \ km$

In summary, for the first conversation, the car's average speed must be 85.45 km/h in order to travel 235 km in 2.75 hours. For the second conversation, the average velocity of the particle over the time interval is approximately 0.57 cm/s. It can be calculated because the time interval is finite. For the third conversation, a bird flying at a speed of 25 km/h would take approximately 8.4 minutes to fly 3.5 km. Time can be calculated using the distance divided by the rate.
  • #1
karush
Gold Member
MHB
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1 What must your car’s $V_{av}$ be in order to travel $\textbf{235 km}$ in $\textbf{2.75 h}$
\begin{align*}\displaystyle
V_{av}&=235km/2.75h \, km/h \\
&=\color{red}{85.45 \, km/h}
\end{align*}

2 A particle at $t_1 =–2.0 s$ is at $x_1 = 4.8 cm$ and at $t_2 = 4.5 s$ is at $x_2 = 8.5 cm$.}\\
i. What is its average velocity over this time interval?\\
ii. Can this be calculated. Why or why not?
\begin{align*}\displaystyle
v_{av}&=\frac{x_2-x_1} {t_2-t_1}\\
&=\frac{8.5-(4.8)}{4.5-(-2.0)}\\
&\approx \color{red}{.57}
\end{align*}

3 A bird can fly $25 km/h$.
How long does it take to fly $3.5 km?$\begin{align*}\displaystyle
D&=R \cdot T\\
\therefore \frac{D}{R}&=T \\
\frac{25}{60}=\frac{5}{12}&=\frac{3.5}{min}\\
5 \ min&=3.5(12) \\
T&=.7(12)=\color{red}{8.4 \, min}
\end{align*}

Ok I know these are relatively easy problems but they will get harder fast,
there is no book anwswer this is from a class that is already over.
I am trying to format these problems so that they look like a math textbook solution
So suggestions are very welcome.
#2 has a negative time in it but I assumed it could be calculated anyway$$\tiny\textit{Embry-Riddle Aeronautical University Dept of Physical Sciences, HW $\# 1-3$ PS 103 / Technical Physics I}$$
 
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  • #2
1. Correct
2. Correct, might want to include units.
3. Correct.
 
  • #3
Rido12 said:
1. Correct
2. Correct, might want to include units.
3. Correct.

$\begin{align*}\displaystyle
v_{av}&=\frac{x_2-x_1} {t_2-t_1}\\
&=\frac{8.5-(4.8)}{4.5-(-2.0)}\\
&\approx \color{red}{.57 \, cm/s}
\end{align*}$
 

Related to Eb3 Velocity and Time: Calculate $V_{av}, v_{av}$, and Time to Fly $3.5 \ km$

1. How do you calculate average velocity (Vav) in the context of EB3 velocity and time?

The formula for average velocity is Vav = ∆x/∆t, where ∆x represents change in distance and ∆t represents change in time. In the context of EB3 velocity and time, you would use the distance of 3.5 km and the time it takes to fly that distance to calculate Vav.

2. What is the difference between average velocity (Vav) and instantaneous velocity (vav)?

Average velocity (Vav) is a measure of the overall displacement or change in position over a certain time period. Instantaneous velocity (vav), on the other hand, is the velocity at a specific moment in time. In other words, Vav is an average over a period of time, while vav is a specific velocity at a specific time.

3. How do you calculate instantaneous velocity (vav) given the average velocity (Vav) and acceleration (a)?

The formula for calculating instantaneous velocity is vav = Vav + at, where a is the acceleration and t is the time at which you want to calculate the velocity. Essentially, you add the product of acceleration and time to the average velocity to get the instantaneous velocity at a specific time.

4. Can you use the same formula to calculate velocity at different points in time?

No, you cannot use the same formula to calculate velocity at different points in time. The formula for average velocity (Vav = ∆x/∆t) is only applicable for calculating the average velocity over a specific time period. To calculate instantaneous velocity at different points in time, you would need to use the formula vav = Vav + at, as mentioned in the previous question.

5. How does time affect the calculation of velocity in the context of EB3 velocity and time?

Time is a crucial factor in calculating velocity. The longer the time period, the greater the potential for change in distance, leading to a higher average velocity. In the context of EB3 velocity and time, time is used to calculate both average velocity and instantaneous velocity, as shown in the formulas Vav = ∆x/∆t and vav = Vav + at.

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