the velocity v of a particle in the xy plane is given by v59

the velocity v of a particle in the xy plane is given by v=(5.9t-4.9t^2)i +8.6j with v in meyers per second and t <0 in seconds at t=4.3 s and in unit vector notatio ,what are
a) the x component of the acceleration?
b)the y component of the acceleration?
c)when is the acceleration zero?
d)at what positive time does the speed equal 10m/s?

Solution

V = (5.9t-4.9t^2)i +8.6j

a = dv/dt = (5.9-9.8*t)i + 0 j

a) ax at t = 4.3 sec = 5.9 - 9.8*4.3 = -36.24 m/s^2

b) ay = 0

c) a = 0 =>   (5.9-9.8*t) = 0 , => t = 5.9/9.8 = 0.602 sec

d)

V = (5.9t-4.9t^2)i +8.6j

=> speed = sqrt ( (5.9t-4.9t^2)^2 + 8.6^2 ) = 10^2

=> (5.9t-4.9t^2)^2 = 10^2 - 8.6^2

=> 5.9t-4.9t^2   = 5.1029

time is imaginary from the above equation which mean for no real time speed becomes 10 m/s