A science fair poster is a rectangle 46 inches long and 36 inches wide. What is the area of the poster in square feet?

Suppose the position of an object moving horizontally after t seconds is given by the following functions s=f(t), s equals f , o

Scilla [17]

Answer:

(a) The graph of position function is shown below.

(b) The velocity function is $v(t)=-2t+4$ and the graph of position function is shown below. The object is stationary at t=2, moving to the right at t>2, and moving to the left at t<2.

(c) Velocity and acceleration of the object at t=1 are 2 and -2 respectively.

(d) The acceleration of the object is -2 when its velocity is zero.

(e) The speed is not increasing at any interval because the acceleration is constant.

Step-by-step explanation:

(a)

The given function is

$f(t)=-t^2+4t-3; 0\leq t\leq 5$

The position of an object moving horizontally after t seconds is given by

$s=f(t)=-t^2+4t-3$

The graph of position function is shown below.

(b)

Differentiate the position function with respect to time to find the velocity function.

$v=f'(t)=-2t+4$

Put v=0 to find the time when the object is stationary.

$0=-2t+4$

$2t=4$

$t=2$

The object is stationary at t=2 because the velocity of the object is 0 at t=2.

The velocity function is $v(t)=-2t+4$ and the graph of position function is shown below. The object is stationary at t=2, moving to the right at t>2, and moving to the left at t<2.

(c)

The velocity function is

$v=f'(t)=-2t+4$

Substitute t=1 in the above function.

$v=f'(1)=-2(1)+4=2$