Friday

November 28, 2014

November 28, 2014

Posted by **Todd** on Friday, July 20, 2012 at 1:52pm.

- Math -
**Reiny**, Friday, July 20, 2012 at 4:32pmif a = 4 - t^2 , then

v = 4t - (1/3)t^3 + c

given: when t=0, v = 2 mm/s

2 = 0 - 0 + c

c = 2

v = 4t - (1/3)t^2 + 2

s = 2t^2 - (1/12)t^4 + 2t + k

when t=0 , s = 0 , so k = 0

s = 2t^2 - (1/12)t^4 + 2t

check by taking the derivative twice

- Math -
**MathMate**, Friday, July 20, 2012 at 4:35pmx"(t)=d²x/da²=a=4-t^2

Integrate two times and substitute the initial conditions to find the required equation:

x'(t)

=∫a dt

=∫(4-t^2)dt

=4t-(t^3/3)+C1

From x'(t)=2 mm-t^-1, we get

2 mm-t^-1 = 4(0)-(0^3/3)+C1

=>

C1=2mm-t^-1

x(t)=∫x'(t)dt

=∫(4t-(t^3/3)+2) dt

=2t²-(1/12)t^4+2t+C2

x(0)=0 => C2=0

=>

x(t)=2t² -(1/12)t^4 +2t

(in millimetres)

**Answer this Question**

**Related Questions**

Physics - A particle moved along the x axis with a constant acceleration of -85....

Maths mst - Question – 3: Consider a particle moving according to the velocity ...

Physics - Starting with the kinematics equation x = vot + ½ at^2, derive an ...

Calc - So I have a particle that is moving along the x-axis. I have the ...

Math - Starting with the kinematics equation x = vot + ½ at^2, derive an ...

differential equation or physics - A particle moves on the x-axis with an ...

physics - A particle has a constant acceleration of a = (5.5 m/s2)i + (3.7 m/s2)...

physics - A particle has a constant acceleration of = (5.5 m/s2) + (3.7 m/s2) . ...

physics - The vector position of a 3.75 g particle moving in the xy plane ...

Algebra HELP! - Starting with the kinematics equation x = vot + ½ at^2, derive ...