Question

A set of keys slides along the floor, coming to rest 3 meters from where they started. If the initial speed of the keys was 1.9 m/s then what is accel. and time?

Please show equations used

Answer 1

We have couple equations we could use:
we know \(\Delta x=3m\) and we know that \(v_0=v_i=1.9m/s\) right?

Answer 2

oh ok. srry my computer didnt show your answer at first. so inital velocity equals velocity?? why is that?

Answer 3

?

Answer 4

hello? this is urgent srry,

Answer 5

hello?

Answer 6

We can use the following kinematics equation:\[\large \bf d=\frac{v_i+v_f}{2} \times t\]Where 'd' represents displacement. We know that \(\bf d = 3m, v_i=1.9m/s\). We also note that the final velocity, i.e. \(\bf v_f=0m/s\) because the keys stop after displacing 3 metres. Plug these values in to the equation will allow us to solve for 't':\[\bf 3m=\frac{(1.9m/s)+(0m/s)}{2} \times t \implies t = \frac{6m}{1.9m/s}=6\cancel{m} \times \frac{ s }{ 1.9\cancel{m} }=\frac{ 60 }{ 19 }s\] Now we know the time but we still need to find acceleration. Also note that the acceleration we're asked to find is in fact the "average acceleration" which is the overall change in velocity over time and has the units \(\bf m/s^2\). We know that the change in velocity, i.e. \(\bf \Delta v = v_f-v_i=0-1.9m/s=-1.9m/s\). We also know that this change in velocity occured over a time period of \(\bf \large \frac{60}{19} \small{s}\). Hence the average acceleration is:\[\bf a = \frac{ \Delta v }{ \Delta t }=\frac{ -1.9m/s }{ \frac{ 65 }{ 19 }s }=\frac{ -1.9m }{ s } \times \frac{ 19 }{ 65s }=-\frac{ 361 }{ 650 }m/s^2\]

Answer 7

@jolee

Answer 8

wow thank u i will read over this, i will ask questions soon. thank u!

Answer 9

so velocity is equal to average velocity?

Answer 10

Oh shoot. I messed up the last calculation for 'a'; the time was supposed to be 60/19 s but I accidentally typed in 65/19 s. The correct calculation should be:\[\bf a=\frac{ \Delta v }{ \Delta t } =\frac{ -1.9m/s }{ \color{red}{\frac{ 60 }{ 19 }s} }=\frac{ -1.9m }{ s } \times \frac{ 19 }{ \color{red}{60 s} }=\color{red}{-\frac{ 361 }{ 600 }m/s^2}\]

Answer 11

@jolee

Answer 12

The red parts indicate the areas where I corrected mistakes/made changes. @jolee

Answer 13

i cant thank you enough. so clarification:

Answer 14

(initial velocity plus final velocity)/2=average velocity=velocity?