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2007-mt1 - Q.1 a In a one-dimensional problem calculate the...

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Q.1 a) In a one-dimensional problem, calculate the velocity of a particle of mass m =500g, at t= 6 t under the influence of a time- dependent force as given graphically. (Consider that the initial velocity of the particle is zero) b) Express the time dependence of velocity on time, ) ( t v , in the interval 1 = t s to 3 = t s. (0,0) F(t) (N) -F 0 t F 0 2.5 F 0 s 1 2 0 = = t N F t (s)

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Q.2 The position of a particle as a function of time is given as ( ) [ ] ( ) j t R i t R t r ˆ sin ˆ cos 1 ) ( ω ω + + = G ; where R and ω are some constants. a) Determine the instantaneous velocity vector, ) ( t v G (using unit vectors ˆ ˆ and i j ) b) Determine the instantaneous acceleration vector , ( ) a t G (using unit vectors ˆ ˆ and i j ) c) What is the mathematical relation between their magnitudes, a G and v G ? d) Determine the vector (cross) product of ) ( t v G and ). ( t a G What is the angle between ) ( t v G and ? ) ( t a G e) Based on the information obtained in previous parts, what is the name for this particular motion? A useful identity: 2 2 sin cos 1 θ θ + =
Q.3 Consider a penalty kick illustrated in the figure.

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2007-mt1 - Q.1 a In a one-dimensional problem calculate the...

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