The velocity function (in meters per second) is given for a particle moving along a line. v(t) = 3t − 8, 0 ≤ t ≤ 3(a) find the displacement.(b) find the distance traveled by the particle during the given time interval.

a) - 10.5 m

b) 10.83 m

Step-by-step explanation:

Given:

Velocity function , v(t) = 3t - 8,      0 ≤ t ≤ 3

a)

For displacement, integerating the function form time 0 to 3

thus,

=

or

Displacement  =

or

Displacement  =

= - 10.5 m

b) For total distance, let us first find the intervals where the velocity went from positive to negative

thus,

3t - 8 = 0

t =

the velocity changed it direction

thus,

we have the interval for speed as t ∈

therefore,

total distance =  [/tex]

=

=  

=

=

= 10.83 m

a² + b²= c²

24² + 7² = c²

c= 25