Rectilinear Motion: Solving for t=0 Velocity

[xzibition8612]

Homework Statement

A point Q in rectilinear motion passes through the origin at t=0, and from then until 5 seconds have passed, the acceleration of Q is 6 ft/s^2 to the right. Beginning at t=5 seconds, the acceleration of Q is 12t ft/s^2 to the left. If after 2 more seconds point Q is 13 feet to the right of the origin, what was the velocity of Q at t=0?

Homework Equations

The Attempt at a Solution

Assume right is positive and left is negative.

t=0 to t=5
x''=6
x'=6t+(V0)
x=3t^2+(V0)t

From t=5 onwards
x''=-12t
x'=-6t^2+(V1)
x=-2t^3+(V1)t+[75+5(V0)t] (parts in brackets [] obtained by using the x=3t^2+(V0)t equation setting t=5)

we are given 13=-2t^3+(V1)t+[75+5(V0)t] at t=7s (from beginning) or t=2s (considering the equation changes at t=5)

thus plugging in t=2 (since x''=-12t begins at t=5) get:

-46=2(V1)+10(V0)

Now need another equation to solve variables. Equating the equations x'=6t+(V0) (t=0 to t=5) and the equation x'=-6t^2+(V1) (t=5 onwards)

Thus plug in t=5 for x'=6t+(V0) and t=0 for x'=-6t^2+(V1) and then equate them to get

30+(V0)=V1

Solve and get V0 = -8.83 ft/s

Book says answer is 2ft/s to the right.

Something went terribly wrong...

 

[tiny-tim]

hi xzibition8612!

hmm … this is exactly why you should never take short-cuts …

t=0 to t=5
x''=6
x'=6t+(V0)
x=3t^2+(V0)t

From t=5 onwards
x''=-12t
x'=-6t^2+(V1)
x=-2t^3+(V1)t+[75+5(V0)t] (parts in brackets [] obtained by using the x=3t^2+(V0)t equation setting t=5)

that 5(V0)t should be 5V0, shouldn't it? …

in between those two paragraphs, you should have paused to state explicitly the final values of x and v, that you intend to use later​

 

[xzibition8612]

Yuo're right. But then I get 2(30+V0)+5(V0)=-46

Hence V0 = -15 m/s

which is still wrong. No idea where i went wrong.

 

[tiny-tim]

hi xzibition8612!

it's very difficult to check your work

(i don't see a 7³ anywhere)

can you write it out in one continuous proof?​

(and please try using the X² button just above the Reply box, instead of ^ )

 

[xzibition8612]

tiny-tim did you get 2 ft/s as the correct answer? If you did, can you just show me how to do it? Because I'm afraid its very difficult to communicate online and if I see what you did then I can figure out where I went wrong thanks.