acceleration?

Question

A space vehicle accelerates uniformly from 65m/s at t=0 to 162m/s at t=10.0s. How far did it move between t=2.0s and t=6.0s?

I'm having problems on how to find the positions for 2.0s and 6.0s.

Answer 1

Definition of average acceleration

a= (v2 - v1)/(t2-t1)

also
in general
S=S0 + V0t + 0.5 a t^2
S0=0 and V0=0

dS=S2- S1
S2=0.5 a t2^2
S1=0.5 a t1^2

first
a= (162 - 65)/(10.0 - 0.0)=9.7m/s^2

S2= 0.5 x 9.7 x (6.0)^2=175m
S1= 0.5 x 9.7 x (2.0)^2=19.4m

finally

dS= 175 - 19.4= 155.6 m