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A particle starts form the origin at t=0 with an initial velocity having an x compoent and a y component. the particle moves in the xy plane with an x component of acceleration only

a)

Determine the components of velocity vector at any time and the total velocity vector at any time

Given Info: Vxi=20m/s, Vyi=-15m/s, Ax=4.0m/s^2, Ay=0.

Solved.

Answer: Vf=Vxi+Vyi = [(20+4.0t)(i hat symbol?) - 15(j hat symbol?)]m/s

b) calculate the velocity and speed of the particle at t=5?

Ok the tricky part... both velocity and speed have the same magnitude because with 2 dimensions you have to use the pythagorean theorm to add the magnitude of the x and y components. I also concluded that vector = speed but with theta(direction).

solved the problem for part B.

c) determine the x and y coordinate of the particle at any time t and the position vector of this time.

xf=vit=1/2at^2= (20t+2.0t^2)m

yf=vit=(-15t)m

so the position vector at any time t is [(20t+2.0t^2)i -15tj]m

Then the example question says.. lets test it out. and gives me some values

at t=5, x=150, y=-75

what is the magnitude of the displacement?

rf=sqrt[(150^2+(-75)^2]=170m

"note that this isnotthe distance that the particle travels in this time! Can you determine the distance from the available data?

Now how do you determine the distance at t=5 ? do you just add the vector components of distance? If someone can please answer that last question, i could rest my mind

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# Vectors: Motion in a plane

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