10. The position of an object moving in a straight line is given by x=4t-2t^2 where x is in meters and t in seconds. a) What is the position of the object at t=2 and 4 s? (10 points) b) What is the instantaneous velocity at t=2 (10 points)

Question

Answer 1

a) To find the position of the object at

and

seconds, we can substitute these values into the equation

.For

:

metersFor

:

metersTherefore, the position of the object at

seconds is 0 meters, and at

seconds is -16 meters.b) To find the instantaneous velocity at

, we need to find the derivative of the position function

with respect to time

. The derivative of a function gives us the rate of change of the function at a specific point.The derivative of

is:

Now, we can substitute

into the derivative to find the instantaneous velocity:

meters per secondTherefore, the instantaneous velocity of the object at

seconds is -4 meters per second.

Soru