A web page designer creates an animation in which a dot on a computer screen has

Question

A web page designer creates an animation in which a dot on a computer screen has a position of r =[ 4.1 cm +( 2.9 cm/s2 )t2]i^+( 5.5 cm/s )tj

Part A

Find the average velocity of the dot between t=0 and t=2.0s .

Give your answer as a pair of components separated by a comma. For example, if you think the x component is 3 and the y component is 4, then you should enter 3,4. Express your answer using two significant figures.

Part B

Find the instantaneous velocity at t=0 .

Give your answer as a pair of components separated by a comma. For example, if you think the x component is 3 and the y component is 4, then you should enter 3,4. Express your answer using two significant figures.

Part C

Find the instantaneous velocity at t=1.0s .

Give your answer as a pair of components separated by a comma. For example, if you think the x component is 3 and the y component is 4, then you should enter 3,4. Express your answer using two significant figures.

Part D

Find the instantaneous velocity at t=2.0s .

Give your answer as a pair of components separated by a comma. For example, if you think the x component is 3 and the y component is 4, then you should enter 3,4. Express your answer using two significant figures.

Explanation / Answer

A) r (t) = (4.1 + 2.9t^2 )i + 5.5 t cm

r(0) = 4.1i + 0j cm

r(2) = 15.7i + 11 j cm

Average velocity = r(2) - r(0) / deltat

= (15.7i + 11 j) - (4.1i + 0j) / 2

= 5.8i + 5.5 j cm/s

<v> = 5.8cm/s, 5.5 cm/s

B) v = dr/dt

v(t) = 5.8t i + 5.5 j cm/s

v(0) = 0i + 5.5j cm/s

ans. 0 , 5.5 cm/s

c) v(1) = 5.8i + 5.5 cm/s

Ans = 5.8, 5.5 cm/s

D) v(2) = 11.6, 5.5 cm/s

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