The vector position of a particle varies in time according to the expression r w

Question

The vector position of a particle varies in time according to the expression r with arrow = 4.20 î 5.00t2 where r with arrow is in meters and t is in seconds. (a) Find an expression for the velocity of the particle as a function of time. (Use any variable or symbol stated above as necessary.) v with arrow = m/s (b) Determine the acceleration of the particle as a function of time. (Use any variable or symbol stated above as necessary.) a with arrow = m/s2 (c) Calculate the particle's position and velocity at t = 2.00 s. r with arrow = m v with arrow = m/s

Explanation / Answer

a)

r = (4.2) i - (5*t^2) j

Now, velocity, v = dr/dt

So, v = d(4.2)/dt i - d(5*t^2)/dt j

So, v = 0 i - (10*t) j <---- answer

b)

a = dv/dt

= (0) i - (10) j <------ answer

c)

Position at t = 2s, r1 = 4.2 i - 5*2^2 j

= ( 4.2 i - 20 j ) m/s

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