A particle has initial velocity, #v = 3hati + 4hatj# and a constant force #F = 4hati - 3hatj# acts on it. The path of the particle is?

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Answer 1 · 2018-02-16T08:44:19

See below.

Assuming no gravity

#ddot p = F/m rArr dot p = F/m t + C_0#

but #dot p(0) = F/m 0 + C_0 rArr C_0 = (3,4)#

and finally

#p = (x,y) = 1/2 F/m t^2+C_0 t + C_1# then

# x = 1/2 4/m t^2+3t+C_1^x#
#y = -1/2 3/m t^2+4t+C_1^y#

and now equating for #t# we get as one of the feasible paths

#16(y-C_1^y)+75m+12(x-C_1^x)-25sqrtm sqrt(8(x-C_1^x)+9m)=0#

Attached a plot for #m=1# and #C_1=(0,0)#

enter image source here