Average velocity of vehicle

[xzibition8612]

Homework Statement

A vehicle accelerates from 2 m/s to 26 m/s in 12 seconds. Determine the acceleration. Also find the average velocity and the distance travelled.

Homework Equations

Average velocity = Total distance/ time taken

The Attempt at a Solution

Acceleration = (26-2)/12 = 2m/s²
Average velocity = ?

Ok the answer for average velocity is = (26+2)/2 = 12.
Total distance = 14*12 =168m.

My question is how is the average velocity computed like this?? WHy 26+2? And why divided by 2? Isn't the total time taken 12 seconds? SHouldn't it be divided by 12? ANy help would be Appreciated.

 

[SammyS]

Homework Statement

A vehicle accelerates from 2 m/s to 26 m/s in 12 seconds. Determine the acceleration. Also find the average velocity and the distance travelled.

Homework Equations

Average velocity = Total distance/ time taken

The Attempt at a Solution

Acceleration = (26-2)/12 = 2m/s²
Average velocity = ?

Ok the answer for average velocity is = (26+2)/2 = [STRIKE]12[/STRIKE] 14 m/s.
Total distance = 14*12 =168m.

My question is how is the average velocity computed like this?? WHy 26+2? And why divided by 2? Isn't the total time taken 12 seconds? SHouldn't it be divided by 12? ANy help would be Appreciated.

The average velocity can be computed like that only if acceleration is uniform (constant). Also, if the acceleration were not constant, all the could be computed in this problem is average acceleration.

 

[xzibition8612]

but why divided by 2? So if acceleration is constant its always divide by 2?

 

[xzibition8612]

damn I'm so goddamn stupid not to understand this

 

[Nickie]

The average velocity is computed by adding the initial velocity (2 m/s) and final velocity (26 m/s) and then dividing by 2. This is because the average velocity is the average of the initial and final velocities. The total time taken (12 seconds) is not used in this calculation because it is already taken into account in the acceleration calculation.

To better understand this, let's look at the formula for average velocity: average velocity = total distance/total time taken. In this problem, we have already calculated the total distance (168 m) and the total time taken (12 seconds), so we can plug those values into the formula: average velocity = 168 m/12 s = 14 m/s. This is the average velocity of the vehicle over the entire 12 seconds, but we are looking for the average velocity between the initial and final velocities. This is why we add the initial and final velocities and divide by 2, as we did in the attempt at a solution.

In summary, the average velocity is computed by adding the initial and final velocities and dividing by 2, because it represents the average of those two velocities over the entire time period. The total time taken is not used in this calculation because it is already taken into account in the acceleration calculation. I hope this helps clarify the concept for you.