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## Homework Statement

A particle moves along a straight line so that its acceleration

*t*seconds after passing a fixed point

*O*on the line is (2 - 2

*t*) cm/s

^{2}. Three seconds after passing

*O*, the particle has a velocity of 5 cm/s. Find and expression, in terms of

*t*, for the velocity of the particle after

*t*seconds.

## Homework Equations

*a = dv/dt = d*

^{2}x/dt^{2}## The Attempt at a Solution

From the information,

*a*= -2

*t*+ 2 when x = 0, and therefore, by anti-differentiating,

*v*= -

*t*+ c.

^{2}+ 2tI assume that the acceleration of the particle stays at -2

*t*+ 2 cm/s

^{2}for the rest of its motion, and so tried substituting (

*t +*3) in for

*t*to get: -2

*t*- 4, the acceleration of the particle after 3 seconds. Here I got stuck. Do I set up simultaneous equations and eliminate? Have I done my anti-differentiation wrong?

Any help appreciated,

Smeato