A particle moves along the +ve x-axis. At time t seconds after leaving a fixed point O from rest, the displacement of the particle from O is

*x* cm.

The acceleration,

*a* cm s^(-2) of the particle is defined by

*a* = { 5 - 3

*t* , 0 <=

*t* <= 1

-(4

*x*+1),

*t*>1

Find

(a) the maximum velocity of the particle and its distance from O when this happens

(b) the speed of the particle when x = 2.5

The acceleration of the particle is defined as a piece-wise function.

Forgive me for the rather unclear mathematical expressions. I'm new here and still learning the ropes of LATEX.

Btw, I calculated the maximum velocity to be 0.5 cm per second at distance 0.25 cm from O.

But the answer given is 3.5 cm per second at distance 2 cm from O.

Need help for both (a) and (b) !

Thank you!