A particle moves along the x-axis with velocity v(t) = t2 - 1, with t measured in seconds and v(t) measured in feet per second. find the total distance travelled by the particle from t = 0 to t = 2 seconds. 0.667 4 none of these 2

0.667 feet

Step-by-step explanation:

To get the total distance travelled, we would integrate the velocity v(t) equation with respect to time t.

Given that the particle moves from t = 0 to t = 2 seconds

Integrating v(t) = t2 - 1

we get

= t^3/3 - t

substituting the boundaries from t = 0 to t = 2 seconds, we get

= 2^3/3 - 2 - (0^3/3 - 0)

= 8/3 - 2 - 0

= 0.667 feet

1.4

2.3

step-by-step explanation:

the formula for the constant of variation is

y= kx

divide each side by x

y/x =kx/x

y/x =k

we know a and y

1.   y/x = k

4/1 =4

check the other values to make sure they are the same

8/2 = 4   12/3 =4   and 16/4 =4  

the constant of variation is 4

2.   y/x = k

3/1 =3

check the other values to make sure they are the same

6/2 = 3   9/3 =3   and 12/4 =3  

the constant of variation is 3

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step-by-step explanation: