Math In Focus - Ex 6.10 Q17) could someone please show the working for this question? (1 Viewer)

[Diamondhead74512]

A particle moves in a line so that its acceleration is given by d2x/dt2 = 8 - 2x. Initially, the particle is at the origin and has velocity 3√2ms-1;

Find the interval in which the particle will travel,

The answers are x=-1 and x=9

I just wanted to know the steps that got to the answers

Thank you!

 

[jazz519]

Re: Math In Focus - Ex 6.10 Q17) could someone please show the working for this quest

a=2(4-x)

d/dx (v^2/2)=2(4-x)
V^2/2=8x-x^2+c
V^2=16x-2x^2+k

Sub v=3root2,x=0

So k=18

V^2=16x-2x^2+18

At end points v=0

0=16x-2x^2+18

Solve and x=-1 and x=9

 

[Diamondhead74512]

Re: Math In Focus - Ex 6.10 Q17) could someone please show the working for this quest

Thank you so much! Had been at the question for ages and was stopping me from doing other work