How to Find Original Speed and Acceleration of a Truck Slowing Down

[chocolatelover]

Homework Statement

A truck covers 45.0 m in 8.50 s while smoothly slowing down to a final speed of 2.20m/s
a. Find its original speed
b. find its acceleration

Homework Equations

average velocity=xf-xi/change in t
average acceleration=vf-vi/chang in t
final velocity=vi+at

The Attempt at a Solution

____________________________

0 8.5 s
2.20m/s

x-2.20m/s/(8.5-0s)

I know that the entire distance is 45.0 m. I don't think I can use any of the three formulas mentioned above, but I'm not sure which other one I could use. Could someone please show me what formula I need or give me a hint, please?

Thank you very much

 

[e(ho0n3]

Since the truck is "smoothly slowing down", the acceleration must be constant and negative.

There are many nice formulas involving distance and speed with constant acceleration. Which ones do you know?

 

[XxBollWeevilx]

You're on the right track with some of the formulas you wrote. Think kinematics.

 

[chocolatelover]

Thank you very much

I know that vf=vi+at, so vi must be=vf-at

acceleration=vf-vi/change in time

Therefore, vi=vf-[(vf-vi)/(change in time)*(t)] right? This doesn't seem to help.

I know that vf=2.20m/s and the change in time is 8.5. It seems that I need to know what vi or a is. 2.20m/s=vi+a(8.5) or would it just be v=d/change in time? vi=45/8.5=5.3
vf=vi+at
2.2=5.3+a(8.5)
a=-3.65

Could someone please explain to me how I could find vi, if I don't know what the acceleration is, please?

Thank you very much

 

[cse63146]

You would just use this formula

d=\frac{V_i+V_f}{2}*t

 

[chocolatelover]

Thank you very much

Does this look right?

d=vi+vft/2

45=vi+2.2m(8.50)/2

vi=71.3

a=vf-vi/t

a=2.2-71.3/8.5
=-8.13

Thank you

 

[cse63146]

sorry didnt realize how the equation came out. You multiply time t by (V_f+V_i)/2

 

[chocolatelover]

It's okay. Does this look right now?

45=8.5vi+18.7/2

vi=8.34

a=2.2-8.34/8.5=-.72

Thank you

 

[cse63146]

Looks good to me, but I would get another person to check it just in case because I could be wrong.

 

[chocolatelover]

Thank you very much

Regards