How Do You Calculate the Average Acceleration of an Eraser in a Physics Problem?

[nadino1992]

Homework Statement

Jordyn throws an eraser at her teacher, it moves horizontally at 8m/s when the teacher smacks it with a metrestick. The eraser leaves the metrestick horizontally at 15 m/s [N30W]. It is in contact with the stick for 0.03s. Determine the average acceleration of the eraser while being hit by the metrestick. Draw a vector diagram showing the motion.

Homework Equations

We were not given specific equations for this question, but since we are given two velocities, time, and are asked for average acceleration, i figured that maybe a=(V1-V2)/t might work.

The Attempt at a Solution

So, first i thought that i could use the equation above, and just plug in the given information, but then i figured that the eraser stopped when it hit the stick. So, it would go from 8m/s to 0m/s and then to 15m/s. I then used two equations (both being a=(V1-V2)/t). For the first, i used V1=8m/s and V2=0m/s; for the second, i used V1=0m/s and V2=15m/s. Since we have to find the average acceleration, i thought maybe i could average out both answers from the two equations. I doubt this works though, maybe it does, I'm not sure. It seems too simple. Especially because i don't know if it's right to use the same time for both equations. Also, i have absolutely no idea how this relates to vectors. If i had to add/subtract both vectors then i could have just drawn that, but they're two separate things. Please help and thanks so much!

 

[rallizes]

i didn't read your attempt cause I am really sleepy and the paragraph is really big but

you want to say the eraser went from 8m/s to 15m/s in the other direction in .3 seconds.

so use kinematics equation vfinal=vinitial+at, so vfinal=-vinitial+a(t), a=(vfinal+vinitial)/(time). vinitial is the opposite sign of vfinal as it is in the opposite direction. you might have that written down i dunno. don't worry about the instantaneous velocity of the eraser cause it asks for the average acceleration, i confused myself the other day cause i thought another problem implied infinite acceleration by saying something stopped right away

 

[nadino1992]

So i completely ignore the fact that it stops and has a velocity of 0m/s while the stick hits it? And for the vector diagram that i draw, do i just just draw 8m/s minus 15m/s[N30W]? Also you said i can just make Vfinal opposite of Vinitial, but they're not in the opposite direction though, one's south and the other is N30W

 

[rallizes]

OH i didn't see the degrees part. you want to split it up into vector components then, where -8=15cos30+at i think if the angle looks like i think it does. and also 0=15sin30+at for the x-component of the acceleration and your answer will be a vector with x and y components? I'm pretty sure you don't need to think about the eraser stopping, and that all you neeed is to think ok it goes from 8m/s in this direction and accelerates to 15m/s in this direction in .3 seconds