A. Find an expression for the velocity of the particle as a function of time. (U

Question

A. Find an expression for the velocity of the particle as a function of time. (Use any variable or symbol stated above as necessary.)

B. Determine the acceleration of the particle as a function of time. (Use any variable or symbol stated above as necessary.)

C. Calculate the particle's position and velocity at t = 5.00 s.

The vector position of a particle varies in time according to the expression r = 8.60 i^ ? 5.00t2 j^ where r is in meters and t is in seconds. Find an expression for the velocity of the particle as a function of time. (Use any variable or symbol stated above as necessary.) Determine the acceleration of the particle as a function of time. (Use any variable or symbol stated above as necessary.) Calculate the particle's position and velocity at t = 5.00 s.

Explanation / Answer

because the OX component of the position vector is time independent. For the OY component of the speed we have

r = (8.60 i - 5.00t^2 j) m
v = dr/dt = -10.00t j m/s

and for acceleration OX component is zero.
a = dv/dt = -10.00 j m/s^2

part c)
at t = 5.00 s
r = (8.60 i - 5.00*5.00^2 j) m

r= (8.60i - 125j)m

velocity

v = -10.00*5.00 j m/s

v= -50.00j m/s

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