posted by Hannah on .
An ant moves along the x-axis with velocity given by v(t)=tsin(t^2), t is greater than or equal to zero.
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
This 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)dt = ∫tsin(t²)dt
Integral of velocity gives distance
For the right-hand side, substitute u=t^2,
x(0)=-cos(0)+C = 3
Distance travaelled = x(2)-x(0)=?
Hannah, Anastasia, Carmen,Yuka, Lena, Catalina, Jamima, ...
I appreciate your inventiveness, but please, stop inventing screen names.