Exercise 3.3 A web page designer creates an animation in which a dot on a comput

Question

Exercise 3.3
A web page designer creates an animation in which a dot on a computer screen has a position ofr  =[ 3.7 cm +( 3.0 cm/s2 )t2]i^+( 4.7 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.

v ave =
15.7i,9.4j
  cm/s  

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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.

v  =
3.7,0
  cm/s  

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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.

v  =
  cm/s  

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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.

v  =
  cm/s  

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Explanation / Answer

Here ,

part A )

r = (3.7 + 3 t^2) i + 4.7 t j

for the average velocity

average velocity = x(2) - x(0) /( 2 - 0)

average velocity = ( (3.7 + 3 * 2^2) i + 4.7 *2 j ) - (3.7 i))/(2)

average velocity = 6 i + 4.7 j cm /s

average velocity = (6 , 4.7) cm/s

part B)

v = dr/dt

v = d/dt((3.7 + 3 t^2) i + 4.7 t j)

v = 6 t i + 4.7 j

Now , at t = 0 s

v = 4.7 j m/s

v = (0 , 4.7 ) cm/s

part C)

at t = 1 s

v = 6 *1 i + 4.7 j

v = 6 i + 4.7 j

v =(6 , 4.7) cm/s

instantaneous velocity at t=1 .0s is (6 , 4.7) cm/s

part D)

at t = 2 s

v = 6 *2 i + 4.7 j

v = 12 i + 4.7 j

v = (12 , 4.7) cm/s

instantaneous velocity at t=2.0s is  (12 , 4.7) cm/s

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