Lizard: A lizard is running in a straight line according to the following: xx(tt) = tt3⁄3 − tt2 + tt He starts at tt = 0. (a) Determine vv(tt). (b) When is the lizard at rest? (c) When is the lizard moving in the positive xx direction? (d) When is the lizard moving in the negative xx direction? (e) When does the lizard have zero acceleration?

Explanation:

a ) x ( t ) = t³ / 3 - t² + t

v = dx / dt = 3 t² / 3 - 2 t + 1 = t² -  2 t + 1

b ) lizard is at rest , v( t ) = 0

t² -  2 t + 1  = 0

( t - 1 )² = 0

t = 1

c )

velocity is positive when

t² -  2 t + 1  > 0

( t - 1 ) ² > 0

Here we see that LHS is a square so it is always positive whatever be the value of t

So velocity is always positive or lizard is always moving in positive x direction .

d ) It never moves in negative x direction .

e )

a ( t ) = dv / dt = 2t - 2

t = 1

so it has zero acceleration at t = 0 .