Question

Question 31 (Essay Worth 5 points)

The position of an object at time t is given by s(t) = 6 - 14t. Find the instantaneous velocity at t = 6 by finding the derivative.

Answer 1

For this case we have by definition, that the derivative of the position with respect to time is the velocity, that is to say:

`\frac {d (s (t))} {dt} = v (t)\\\frac {d (6-14t)} {dt} = v (t)`

So:

Taking into account that the derivative of a constant is 0.

`\frac {d (6-14t)} {dt} = 0- (1 * 14 * t ^ {1-1}) = 0- (14 * t ^ 0) = - 14`

So, the velocity is -14

Answer:

-14