An object moves along the x-axis according to the equation x = 3.00t2 – 2.00t + 3.00, where x is in meters and t is in seconds. determine a) the average speed between t = 2.00 s and t = 3.00 s, b) the instantaneous speed at t = 2.00 s and t = 3.00 s, c) the average acceleration between t = 2.00 s and t = 3.00 s, and d) the instantaneous acceleration at t = 2.00 s and t = 3.00 s. e) at what time is the object at rest?

Explanation:

x = 3.00 – 2.00t + 3.00,

Distance of object at 2 second,

x (t=2) = 3(4) - 2(2) +3

x (t=2) = 12-4 +3

x (t=2) = 11 m

Distance of object at 3 second,

x (t=3) = 3(9) - 2(3) +3

x (t=2) = 27 - 6 + 3

x (t=2) = 24 m

a) the average speed between t = 2.00 s and t = 3.00 s,

Average speed =

Average speed =

Average speed =

Average speed =

Average speed = 11.66

b) the instantaneous speed at t = 2.00 s and t = 3.00 s,

Instantaneous speed =

Instantaneous speed(v) = 6t - 2

Instantaneous speed,v(t=2 to t=3) = 18-2-12+2

Instantaneous speed, v = 6

c) the average acceleration between t = 2.00 s and t = 3.00 s

average acceleration =

average acceleration =  

average acceleration = 11.66

d) the instantaneous acceleration at t = 2.00 s and t = 3.00 s

instantaneous acceleration =

instantaneous acceleration =6

instantaneous acceleration = 6

e) for x =0

0 = 3.00 – 2.00t + 3.00

a = 3, b=-2, c=3

t=

t=

t=

general solution of this equation gives imaginary value. Hence, the given object is not at rest.

an electric circuit