Find the velocity of the stock car

[Joe91090]

Homework Statement

A professional race-car driver buys a car that can accelerate at 5.7 m/s^2. The racer decides to race against another driver in a souped up stock-car. Both start from rest, but the stock-car driver leaves 1.4s before the driver of the sports car. The stock-car moves with a constant acceleration of +3.6m/s^2.

A) Find the time it takes the two drivers to travel before they are side by side.
B) Find the distance the two drivers travel before they are side by side.
C) Find the velocity of the race car when the two drivers are side by side.
D) Find the velocity of the stock car when the two drivers are side by side.

Homework Equations

v=u+at

X= ut + 1/2at

quadratic formula

The Attempt at a Solution

My teacher assigns our homework online and we are only allowed a certain number of tries. I used all my tries up for part A so now I can't find B-D without the answer to A.

First I found out what each car was doing in the first 1.4 seconds using x= ut + 1/2at then set them both to equal each other and pluged the times and accelerations into the quadratic formula.

Ive been working on this one problem all week its driving me crazy. PLEASE HELP !

 

[LowlyPion]

I trust you mean that

X= ut + 1/2at²

Remember there is more to that equation, namely

X = Xo + Vo*t + 1/2*a*t²

So your method is ok, but you need to have both the initial speed and position for the car that starts first. I'm not sure you did this by your description.

 

[Joe91090]

Yes I left out the squared and Xo would be zero since they both start from the same pos. and Vo would be zero in one of the cars and the other Vo would be the velocity of the car 1.4s after they started but I still can't get the correct answer

 

[gabbagabbahey]

and Xo would be zero since they both start from the same pos.

So after 1.4 secs, the second car is still at the same positions?

 

[LowlyPion]

Yes I left out the squared and Xo would be zero since they both start from the same pos. and Vo would be zero in one of the cars and the other Vo would be the velocity of the car 1.4s after they started but I still can't get the correct answer

Figure where the first car is at t = 0 of when the second car is going to start. If you don't do that, you will never get the right answer. (Oh and ² the time for the acceleration term.)

 

[Joe91090]

is there a difference in accelertation and constant acceleration ??

 

[LowlyPion]

is there a difference in accelertation and constant acceleration ??

Just use the acceleration in the equations for each car as given.

These accelerations are constant.

It doesn't have to be constant, but they want constant acceleration here.

 

[Joe91090]

Ive taken this problem http://zebu.uoregon.edu/~probs/mech/1dkin/constacc5/node2.html and put in the info from my problem and got a wrong answer did i miss something or would it not work if i did ?

 

[LowlyPion]

Write the equations for this problem. Don't worry about other problems.

It's important you learn to build the equations from scratch. Otherwise you won't understand them. And come exam time I'm thinking that's something you will want to be doing.

 

[Joe91090]

so I've found the stock car has moved 3.528m in those first 1.4s and its velocity is 5.04m/s. So that's Xo and Vo. Would the other cars Xo and Vo be 0 and 0 ?

 

[Joe91090]

I got 9.47s for an answer to part A but I can't check if its right because I've run out of tries. could you please tell me if its right

 

[gabbagabbahey]

so I've found the stock car has moved 3.528m in those first 1.4s and its velocity is 5.04m/s. So that's Xo and Vo. Would the other cars Xo and Vo be 0 and 0 ?

Yes, this looks promising

 

[gabbagabbahey]

I got 9.47s for an answer to part A but I can't check if its right because I've run out of tries. could you please tell me if its right

No, this is incorrect. Show us your work and we'll be able to see what you are doing wrong now.

 

[Joe91090]

0 + 1/2(5.7)t^2 = 3.528 + 5.04t + 1/2(3.6)t^2

2.85t^2 = 3.528 + 5.04t + 1.8 t^2

1.05t^2 - 5.04t - 3.528 = 0

-5.04 +- sqaure root of ( 5.04^2 - 4(1.05)(-3.528) / 2(1.05)

 

[gabbagabbahey]

0 + 1/2(5.7)t^2 = 3.528 + 5.04t + 1/2(3.6)t^2

2.85t^2 = 3.528 + 5.04t + 1.8 t^2

1.05t^2 - 5.04t - 3.528 = 0

-5.04 +- sqaure root of ( 5.04^2 - 4(1.05)(-3.528) / 2(1.05)

Close, b=-5.04 not +5.04 so,

t=[-(-5.04) +- sqaure root of ( (-5.04)^2 - 4(1.05)(-3.528)] / 2(1.05)

 

[Joe91090]

I get 8.37 for a time. is this correct ?

 

[gabbagabbahey]

No, you must be punching things into your calculator wrong...be careful with your brackets!

 

[Joe91090]

and to find the distance i got 199.6m by taking the racer cars info and plugged it into the equation.


x= 0 + 0 + 1/2(5.7)(8.37)^2

 

[gabbagabbahey]

and to find the distance i got 199.6m by taking the racer cars info and plugged it into the equation.


x= 0 + 0 + 1/2(5.7)(8.37)^2

Right idea, but wrong time value...

 

[Joe91090]

i keep getting 8.37

im plugging this in excatly

(-(-5.04)+square root((-5.04)^2-4(1.05)(-3.528))/2(1.05)

 

[gabbagabbahey]

For starters, you need anaother pair of brackets.../2(1.05) divides by 2 and multiplies by 1.05...you want to punch in... /(2*1.05).
You also need another closing bracket after the sqrt

You should get 5.42s

 

[Joe91090]

alright so the distance should be 83.7m ?

 

[gabbagabbahey]

Yes.

 

[Joe91090]

Thank you so much for all the help.

 

[gabbagabbahey]

Welcome