The velocity function (in meters per second) is given for a particle moving along a line. \[ v(t)=3 t-5, \quad 0 \leq t \leq 3 \] (a) Find the displacement (in meters). \[ -1.5, \mathrm{~m} \] (b) Find the total distance traveled (in meters) by the particle during the given time interval $1.5 \times \mathrm{m}$

Step 1 ：The velocity function for a particle moving along a line is given as \(v(t) = 3t - 5\), where \(t\) is the time in seconds and ranges from 0 to 3.

Step 2 ：The displacement of the particle is the integral of the velocity function over the given time interval. In this case, we need to integrate the function \(v(t) = 3t - 5\) from \(t=0\) to \(t=3\).

Step 3 ：The total distance travelled by the particle is the absolute value of the displacement.

Step 4 ：Let's calculate these two values.

Step 5 ：For \(t = t\), \(v = 3t - 5\), the displacement is \(-3/2\).

Step 6 ：The total distance is the absolute value of the displacement, which is \(3/2\).

Step 7 ：Final Answer: The displacement of the particle is \(\boxed{-1.5}\) meters and the total distance traveled by the particle is \(\boxed{1.5}\) meters.