The velocity of a particle at the origin.

[MelissaJL]

Homework Statement

A particle moves according to the position function x(t)=ct²+bt where c=3m/s² and b=-7m/s. Find the velocity at the origin.


2. The attempt at a solution
I tried just taking the derivative and setting t=0 to the equation as so:
v_x(t)=6t-7=6(0)-7=-7 m/s
Although, when I put the answer into WebAssign it says I'm incorrect. I'm not looking for a definite answer since this is my homework but would just like to understand what I am doing wrong.

 

[Hypersphere]

Maybe they're looking for the velocity at the other time the particle is at the origin?

 

[MelissaJL]

I'm under the impression that the origin means they want me to solve it at t=0. What other origin could they be asking for?

 

[Hypersphere]

I guess they mean the origin of the coordinate system, i.e. x=0. You usually say t=0 rather than the slightly ominous "the origin of time".

 

[MelissaJL]

Yeah I just tried now to solve it at x=0 where I find that,
x(t)= 3t²-7t
0=3t²-7t+0constant
Then I treated it like a quadratic:
t=7+√[7²-4(3)(9)] = 7/3s
2(3)
Then I put 7/3s into the formula...and...I got it right, thanks so much.



Answer ends like so,
v_x=6(7/3)-7= 7m/s

 

[Hypersphere]

There is an easier way to solve it, just factor out one of the t's:
x=ct^2+bt = t(ct+b),
for which x=0 when t=0 or t=-b/c. Both solutions are of course valid (based on the problem text), even if the homework website doesn't think so...

 

[marty1]

x(t) = 0 when t=2.3333333333