A particle moves in the xy plane with constant acceleration. At time zero, the p

Question

A particle moves in the xy plane with constant acceleration. At time zero, the particle is at x = 7 m, y = 5.5 m, and has velocity v^rightarrow_0 = (1 m/s) i^cap+ (-8 m/s) j^cap. The acceleration is given by a = (7.5 m/s^2) i^cap + (9 m/s^2) j^cap. What is the x component of velocity after 4 s? Answer in units of m/s. What is the y component of velocity after 4 s? Answer in units of m/s. What is the magnitude of the displacement from the origin (x = 0 m, y = 0 m) after 4 s? Answer in units of m.

Explanation / Answer

from equation of motion

vx = vox + ax*t

vx = 1 + (7.5*4) = 31 m/s

===========================

vy = voy + ay*t

vy = -8 + (9*4) = 28 m/s

++++++++++=

x1 = x + vox*t + (1/2)*ax*t^2

x1 = 7 + (1*4) + (0.5*7.5*4^2)

x1 = 71 m

y1 = y + voy*t + (1/2)*ay*t^2

y1 = 5.5 - (8*4) + (0.5*9*4^2)

y1 = 45.5 m

magnitude = sqrt(x1^2+y1^2) = sqrt(71^2+45.5^2) = 84.3 m

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