Can Someone tell me where I went wrong?

[soccerball3211]

The velocity v of a particle moving in the xy plane is given by v = (5.4 t - 4.1 t^2)(i hat) + 8.4(j hat), with v in meters per second and t (> 0) in seconds. (a) What is the acceleration when t = 3.7 s? (b) When (if ever) is the acceleration zero? (c) When (if ever) does the speed equal 10 m/s?

Here are my answers
a.) -25 m/s^2
b.) .66 s
c.) .87 s

My part C is wrong and I can't figure out why?

Can someone please explain why .87 s is wrong!

 

[stapel]

It will be a lot easier to find where you went wrong (if indeed you did) once you have posted all of your work and reasoning.

Thank you.

Eliz.

 

[galactus]

There will be two answers for part c because of the quadratic.

Maybe that's your trouble.

 

[soccerball3211]

Ok for part a I differentiated the equation with respect to time and came up with:

the acceleration vector = (5.4-8.2t)(i hat)
then i just plugged in 3.7 s for t and came up with -24.94 for part a

then for part b i set the acceleration = 0
0=(5.4-8.2t) (i hat)
then i solved for t and got .66 s

then for part c i set the original velocity vector = 10
thus giving me 10=(5.4t-4.1t^2)(i hat) + 8.4 (j hat)

Then from that I used the quadratic equation and found t to equal .87 and .45

 

[pka]

First of all, you do realize that speed is ||v(t)||?
If we calculate that for 10 we get t= 1.9486663493879420157.

 

[soccerball3211]

Ok for part a I differentiated the equation with respect to time and came up with:

the acceleration vector = (5.4-8.2t)(i hat)
then i just plugged in 3.7 s for t and came up with -24.94 for part a

then for part b i set the acceleration = 0
0=(5.4-8.2t) (i hat)
then i solved for t and got .66 s

then for part c i set the original velocity vector = 10
thus giving me 10=(5.4t-4.1t^2)(i hat) + 8.4 (j hat)

Then from that I used the quadratic equation and found t to equal .87 and .45

 

[pka]

then for part c i set the original velocity vector = 10
thus giving me 10=(5.4t-4.1t^2)(i hat) + 8.4 (j hat) Then from that I used the quadratic equation and found t to equal .87 and .45

No that is incorrect!
The ‘speed’ is the length of the velocity vector!
Therefore, you must find the value of t for which the length of the velocity vector is 10.