A stone is tossed into the air from ground level with an initial velocity of 34

Question

A stone is tossed into the air from ground level with an initial velocity of 34 m/s. Its height at time tt is h(t)=34t4.9t2h(t)=34t4.9t2m.

Compute the stone's average velocity over the time intervals [1,1.01], [1,1.001], [1,1.0001][1,1.01], [1,1.001], [1,1.0001] and [0.99,1], [0.999,1], [0.9999,1].[0.99,1], [0.999,1], [0.9999,1].

(Use decimal notation. Give your answer to three decimal places.)

Estimate the instantaneous velocity at t=1t=1

v=v=  help (decimals)

time interval [1,1.01][1,1.01] [1,1.001][1,1.001] [1,1.0001][1,1.0001] [0.9999,1][0.9999,1] [0.999,1][0.999,1] [0.99,1][0.99,1] average velocity

Explanation / Answer

avg velocity=(integrtion of displacement*dt)/(integration of dt) over a time interval

so,

avg velocity=t(34-4.9t)/t over given time interval=34-4.9t

(1)

[1,1.01]

avg vel=34-4.9(1.01-1)=33.951 m/s

(2)

[1,1.001]

avg vel=34-4.9(1.001-1)=33.995 m/s

(3)

[1,1.0001]

avg vel=34-4.9(1.0001-1)=33.999 m/s

(4)

[.9999,1]

avg vel=34-4.9(1-0.9999)=33.999 m/s

(5)

[.999,1]

avg vel=34-4.9(1-.999)=33.995 m/s

(6)

[.99,1]

avg vel=34-4.9(1-.99)=33.951 m/s

instantaneous valocity at t=1:

34-4.9t=29.1 m/s

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