a particle moves along the x-axis so that anytime t0, it's acceleration is given by a(t)=ln(1+2^t). If the velocity of the particle is 2 at time t=1, then the velocity of the particle at time t=2 is?

a) 0.462
b) 1.609
c) 2.555
d) 2.886
e) 3.346

Question

a particle moves along the x-axis so that anytime t>0, it's acceleration is given by a(t)=ln(1+2^t). If the velocity of the particle is 2 at time t=1, then the velocity of the particle at time t=2 is?

a) 0.462
b) 1.609
c) 2.555
d) 2.886
e) 3.346

anonymous · Answer

please and thank you :)

jamesj · Answer

as dv/dt = a, integrate that expression to find a formula for v(t).  You can use the velocity at t = 1 as an initial condition to find the constant of integration.

anonymous · Answer

I understood that part so far and I integrated the expression and then plugged in the point but didn't get any of the answer choices..

anonymous · Answer

Wait, what do you mean by "You can use the velocity at t = 1 as an initial condition to find the constant of integration."?

jamesj · Answer

you integrate, you have a constant of integration, you use the fact that v(1) = 2 to find the constant of integration and hence you have the complete expression for v(t).

Now evaluate that expression for t = 2

anonymous · Answer

vary well explained

anonymous · Answer

Yup, that was amazing. Thank you :)