The particle travels along the path defined by the parabola y = 0.5x^2, where x

Question

The particle travels along the path defined by the parabola y = 0.5x^2, where x and y are in ft. (Figure 1) If the component of velocity along the x axis is v_x = (2t) ft/s, where t is in seconds, determine the particle's distance from the origin Ot = 3 s. When t = 0, x = 0, y = 0 Express your answer using three significant figures and include the appropriate units. Determine the magnitude of its acceleration when t = 3 s. Express your answer using three significant figures and include the appropriate units.

Explanation / Answer

dx/dt =2t

by integration

x=t2+c ( c is a constant)

using initial condition t=0 x=0 y=0

c=0

t= 3

x= 9 ft

y= 40.5 ft

distance = sqrt(92+40.52) = 41.488 ft.

taking doble derivetives of position.

ax= 2

ay= 6 t2= 54

a= sqrt(542+22)= 54.037 ft/s2

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