Question

CB 2 x c 0 College Board AP Classroom 8.2 PARTICLE MOTION Mala Nou - 6 0 -6-0-0-0-0-0 Question 1 A particle moves along the x-axis. The velocity of the particle at time is given by v(t) 42 If the position of the particle is z - I when t-2, what is the position of the particle when (A) 0.617 B) 0.647 1.353 D ) 5.712

the first pictures equation is 4/(t^3 +1)

Answer 1

$v(t) = \frac{4}{t^3+1}$

from definition of velocity,

$v(t) = \frac{dx}{dt}$

I + 8?_?P dx

integrating both sides wrt t (with limits) ,

$\int_{2}^{4} dx = \int_{2}^{4} \frac{4}{t^3+1} \ dt$

using calculator to find definite integral in RHS,

given x(2) = 1

Thus, position of particle at t = 4 is x = 1.353