Exercises gives the positions s = f(t) of a body moving on a coordinate line, with s in meters and t in seconds. a. Find the body’s displacement and average velocity for the given time interval.
b. Find the body’s speed and acceleration at the endpoints of the interval.
c. When, if ever, during the interval does the body change direction?
s = t^2 - 3t + 2, 0 <= t <= 2

Hi there!

a. Find the displacement by plugging in the values of the interval:

f(2) - f(0) = 0 - 2 = -2 meters.

Average velocity is the slope, thus:

The average velocity for the interval is -1 m/s.

b. To find the speed at the endpoints, we must take the derivative to get the velocity equation:

f(t) = t² - 3t +2

f'(t) = 2t - 3, at t = 0, speed = |-3| = 3 m/s. At t = 2, speed = 2(2) - 3 = 1 m/s.

Acceleration is the second derivative, thus:

f''(t) = 2. The acceleration is 2 m/s² for both endpoints.

c. When the body changes direction, the first derivative changes signs. Thus:

0 = 2t - 3

3 = 2t, t = 1.5 sec. This is where the body changes direction.

solution:

→c= a b , that is product of a and b is possible only when when a is m × n matrix and b is n × p matrix.

that is, number of columns of a= number of rows of b.

so, size of matrix , c= a b is , if a = (m × n)matrix

b= (n × p)matrix

then a b = [ (m × n)matrix] ×[   (n × p)matrix ]

→→c= a b= [m × p ] matrix

→→size of product a b will be equal to = number of rows of a × number of columns of b

yes

step-by-step explanation: