4.20 The position of a particle is given by
r = 3.0t ? − 2.0t 2 ? + 4.0 ? m
where t is in seconds and the coefficients have the proper units for r to be in meters.
(a) Find the v and a of the particle?
(b) What is the magnitude and direction of velocity of the particle at t = 2.0 s?
4.20 The position of a particle is given by
r = 3.0t ? − 2.0t 2 ? + 4.0 ? m
where t is in seconds and the coefficients have the proper units for r to be in meters.
(a) Find the v and a of the particle?
(b) What is the magnitude and direction of velocity of the particle at t = 2.0 s?
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1 Answer
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4.20
(a) The position is given by = 3. 0t ? − 2.0t 2 ? + 4.0 ?
The velocity v is given by = = (3.0t ? − 2.0t 2 ? + 4.0 ?)
= 3.0 ? – 4.0t?
Acceleration = = (3.0 ? – 4.0t?) = – 4.0?
(b) At t = 2.0s
= 3.0 ? – 4.0t?
The magnitude of velocity is given by = (3.02 +- 8.02)0.5 = 8.54 m/s
Direction, = = = 69.44
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Please find the solution below:
after 10 kicks,
v? = 3tî v? = 24cos 60°î + 24sin 60°? = 12î + 12√3?
v? = v? – v? = (12 – 3t)î + 12√3?
It is minimum when 12 - 3t = 0 ⇒ t = 4sec
ω = θ² + 2θ
α = (ωdω)/dθ = (θ² + 2θ) (2θ + 2)
At θ = 1rad.
ω = 3rad/s and α = 12rad/s²
a? = αR = 12 m/s² a? = ω²R = 9 m/s² A? = √ (a? ² + a? ²) = 15 m/s²
a? = v? ²/4r
a_A? = (v? ²/r²) × r = v? ²/r
a_A = 3v? ²/4r
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