How far does a rocket sled move under given acceleration?

[newboo]

A rocket sled for testing equipment under
large accelerations starts at rest and acceler-
ates according to the expression
a = (1.7 m/s3) t + (7.9 m/s2) .
How far does the sled move in the time
interval t = 0 to t = 1.9 s ?

 

[omoplata]

You can use $a = \frac{d^2 x}{d t^2}$.

Just integrate it twice with the appropriate boundary conditions.