Question

Answer Check!! Medal!!
For an object whose velocity in ft/sec is given by v(t) = −t2 + 6, what is its displacement, in feet, on the interval t = 0 to t = 6 secs?

−36 <--
36
0
55.596

Answer 1

Integrate
-1/3x^3+6x
Solve for 6.

Answer 2

-36 is correct.

Answer 3

Given the velocity, preferably expressed as v(t) = −t^2 + 6, integrate with respect to t to obtain a general expression for displacement (it should end in C). Find x(6), x(0) and x(6)-x(0). The latter is the displacement in question.

Or, write the definite integral, as follows:\[\int\limits_{0}^{6}(-t^2+6)dt\] and evaluate it.

Answer 4

displacement is the integral with respect to time, t of velocity.