The position of a particle moving along the x axis is given in centimeters by x = 9.16 + 1.87 t3, where t is in seconds. calculate (a) the average velocity during the time interval t = 2.00 s to t = 3.00 s; (b) the instantaneous velocity at t = 2.00 s; (c) the instantaneous velocity at t = 3.00 s; (d) the instantaneous velocity at t = 2.50 s; and (e) the instantaneous velocity when the particle is midway between its positions at t = 2.00 s and t = 3.00 s.

a)V=17.76 cm/s

b)V=22.44 cm/s

c)V=50.49 cm/s

d)V=35.06 cm/s

e)V=37.63 cm/s

Explanation:

Given that  

a)

When t= 2 s

When t= 3 s

So the average velocity V

V=17.76 cm/s

b)

When know that

So

When t= 2 s

V=22.44 cm/s

c)

At t= 3 s

V=50.49 cm/s

d)

At t= 2.5 s

V=35.06 cm/s

e)

At t= 2 s  ,x=24.12 cm

At t=3 s    x=59.65 cm

So midway of 24.12 cm and 59.65 cm is (24.12+59.65 )/2=41.88 cm

So when x=41.88 cm

t=2.59 s

So velocity

V=37.63 cm/s

c because the action was the roller coaster reaches bottom of hill (action) reaction would be blood tends to drain away from head

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