Friday

October 24, 2014

October 24, 2014

Posted by **Hannah** on Saturday, February 26, 2011 at 10:25pm.

Given that x(t) is the position of the particle at time t and that x(0)=3, find x(2)

Find the total distance traveled by the particle from t=0 to t=2

- Calculus-IVP -
**MathMate**, Saturday, February 26, 2011 at 10:39pmThis is an initial value problem, where you would solve a differential equation (or an integral), and with a given set of initial values, determine the integration constant.

Let x(t)=position at time t

v(t)=tsin(t^2)

∫v(t)dt = ∫tsin(t²)dt

Integral of velocity gives distance

For the right-hand side, substitute u=t^2,

du=2tdt

x(t)=∫(1/2)sin(u)du

=-cos(u)/2+C'

=-cos(t^2)+C

Given x(0)=3

=>

x(0)=-cos(0)+C = 3

C=3+cos(0)=4

=>

x(t)=-cos(t^2)+4

x(2)=4-cos(2^2)=4-cos(4)

Distance travaelled = x(2)-x(0)=?

- Too many screen names -
**MathMate**, Saturday, February 26, 2011 at 10:52pmHannah, Anastasia, Carmen,Yuka, Lena, Catalina, Jamima, ...

I appreciate your inventiveness, but please, stop inventing screen names.

**Answer this Question**

**Related Questions**

Calculus (Answer Check) - Are my answers right? If they are wrong you dont have ...

math - a particle starts at time t = 0 and moves along the x - axis so that its ...

Calculus (Answer Check) - A particle moves along the x-axis so that its velocity...

Calculus (Answer Check) - A particle moves along the x-axis so that its ...

Calculus - a particle starts at time t = 0 and moves along the x axis so that ...

Calculus - A particle moves along the x-axis with the velocity given by v(t)=3t...

calculus - 5. A particle moves along the y – axis with velocity given by v(t)=...

Ap calc - A particle moves on the x axis so that it's position at any time t is ...

HS Calculus - Having trouble with this questions. Please help. A particle moves ...

calculus - 5. A particle moves along the x-axis in such a way that its position ...