If you walked 29752 meters in 2.00 hours what would your average speed be in m/s. then, suppose you slow down to 3.00 m/s at the midpoint, but then pick up again and accelerate to the speed calculated before. it takes you 30.0 s to accelerate. find the magnitude of the average acceleration during this time interval

Explanation:

x = 3.00t^{2} – 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 = \frac{Total distance}{ Total time}

Average speed = \frac{x (t=2) + x (t=3)}{3}

Average speed = \frac{24+11}{3}

Average speed = \frac{35}{3}

Average speed = 11.66 \frac{m}{s}

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

Instantaneous speed = \frac{dx}{dt}

Instantaneous speed(v) = 6t - 2\left \{ {{t=2} \atop {t=3}} \right.

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

Instantaneous speed, v = 6 \frac{m}{s}

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

average acceleration = \frac{average velocity}{time}

average acceleration =  \frac{11.66}{3-2}

average acceleration = 11.66 \frac{m}{s^{2} }

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

instantaneous acceleration = \frac{dv}{dt}

instantaneous acceleration =6

instantaneous acceleration = 6 \frac{m}{s^{2} }

e) for x =0

0 = 3.00t^{2} – 2.00t + 3.00

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

t= \frac{-b \pm \sqrt{b^{2} - 4ac} }{2a}

t= \frac{2 \pm \sqrt{4 - 36} }{6}

t= \frac{2 \pm \sqrt{-32} }{6}

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

Explanation:

Credit goes to @Branta