# How to solve this variable acceleration Q, parts a to c?

##

thank you

thank you

##### 1 Answer

a)

b)

c) see below

#### Explanation:

The expression for the position can be rewritten in the form :

a) The velocity is

Thus the particle is at rest (

b) Since the velocity, which in this case is a continuous function, vanishes at

- displacement between
#t=0# and#t = 1/2# :

#x(1/2)-x(0) = 1/2times (1/2)^2(1/2-1)^2-0#

#qquad = 1/32# - displacement between
#t=1/2# and#t = 1# :

#x(1)-x(1/2) = 0-1/2times (1/2)^2(1/2-1)^2#

#qquad = -1/32# - displacement between
#t=1# and#t = 2# :

#x(2)-x(1) = 1/2times (2)^2(2-1)^2-0#

#qquad = 2#

The distances traveled in these three intervals are

Thus the total distance traveled is

c) It is easy to see that