On a distantplanet, an astronaut threw a ball and quickly wrote down anequation

Question

On a distantplanet, an astronaut threw a ball and quickly wrote down anequation to model its height in meters.

                         s(t) = - (3/4) (t^2) + (29/5)(t) +2

where trepresents the time in seconds after the throw. (Assume thatfractions in the equation are exact.)

a) What wasthe velocity of the ball at t = 2.5 seconds?

b) What wasthe velocity at t = 7.00 seconds?

c) What wasits average velocity from 2.5 to 7 seconds?

d) When wasthe velocity zero?

e) What was its accelerationat t = 7.00 seconds?

* Hint: It’sappropriate to give a direction (up or down) with answers.

Explanation / Answer

s(t) = - (3/4) (t^2) + (29/5)(t) +2
=> velocity v(t)=-3/2*t +29/5 acceleration a=-3/2 m/s2 (a) v(2.5)=2.05m/s (up) (b) v(7s)=-4.7m/s   (down) (c)its average velocity from 2.5 to 7 seconds v=(-4.7-2.05)/(7-2.5)=-1.5 m/s (d)the velocity zero v(t)=0 => t=3.867s (e) its acceleration at t = 7.00 seconds =-1.5 m/s2 (e) its acceleration at t = 7.00 seconds =-1.5 m/s2

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