Question

A particle moves along a straight path with an acceleration that varies with time according to the equation a=2t. The object is initially at rest at the origin. Determine the object's displacement at time t= 2 seconds.

Answer 1

a(t) = 2t
v(t) = t^2 since v(0) = 0
x(t) = 1/3 t^3 since x(0) = 0
Now find x(2)

Answer 2

d^2 x/dt^2 = 2 t
dx/dt = t^2 + 0
x = t^3 / 3 + 0 + 0
when t= 2
x = 8/3