Calculate the average velocity for a remote controlled vehicle that starts with a velocity of 1.0 m/s [forward] and then accelerates at 0.08 m/s2 [backward] for 4.0 s.

Hello!
"Accelerates backward" probably means "decelerates". In other words, the acceleration is - 0.08 m / s^2 while the initial velocity is 1.0 m / s . This way the velocity at a time t seconds is v = v( t ) = 1.0 - 0.08 t .
The average value of this velocity from t = 0 seconds to t = 4 seconds is

1 / 4 int_0^4 (1.0 - 0.08 t) dt = 1 / 4 (t - 0.04 t^2 )_(t=0)^4 =
=1 - 0.01 * 16 = 1 - 0.16 = 0.84 (m / s) .
So, although the velocity of the remote controlled vehicle decreases, it remains positive and its average is also positive, namely 0.84 m /s .