How will an object inside a vehicle move (relative to the vehicle) while the vehicle is making a turn at a constant speed? I understand that the object should continue to move in a straight line (relative to the earth) and therefore should move towards the outside of the turn, but will it be pushed to the front or the back of the vehicle? 
Can the vehicle be considered a frame of reference to apply newtons laws? 
 A: You can imagine the car to be part of a large rotating turntable. You are then asking about the motion of an object relative to the turntable. 
Because the car and turntable are rotating they form a non-inertial frame of reference. You can apply Newton's laws to rotating frames of reference but you need to include two fictitious/pseudo forces in order to explain the motion relative to such frames : these are centrifugal force and Coriolis force. (There is a 3rd fictitious force - the Euler force - which applies if the rotating reference frame has an angular acceleration.) The centrifugal force pushes the object radially outwards. The Coriolis force pushes the object sideways - not tangentially in the rotating frame but perpendicular to the object's velocity in the rotating frame, and in proportion to the magnitude of this velocity.   
The object starts moving radially outwards due to the centrifugal force. As it gathers speed radially the direction of the Coriolis force is initially to the rear of the vehicle. So relative to the vehicle the object initially moves towards the outer side and the rear. Whether it hits the side or the rear depends on the shape of the vehicle and the point of release. 


Suppose there are axes Oxy fixed in the rotating turntable. The object is initially at $(0,r)$ and the object and car are turning anti-clockwise with velocity $v$. After a time $t$ the turntable and axes have turned through angle $\theta=\omega t$ where $\omega=v/r$. The axes have a new orientation Ox'y'. The object at $P$ has moved in a straight line to $P_1'$, while the original position of $P$ in the car has moved distance $s=r\theta$ along the arc to $P_1$. The co-ordinates of $P_1'$ in Oxy are $(-s,r)$ and in Ox'y' they are
$x'=-r\theta\cos\theta+r\sin\theta$
$y'=r\theta\sin\theta+r\cos\theta$.

The graph shows the position of $P_1'$ (blue line) relative to the centre O of the turning circle in the rotating axes Ox'y'. Distances are in units of $r$, the radius OP of the turning circle as measured for P. The motion of $P_1'$ is initially outwards along Oy' but also turning back away from Oy' - ie to towards the rear of the vehicle. 
Whether the object strikes the offside, rear or nearside windows depends on the size of the vehicle relative to the radius of the turning circle. These outcomes are illustrated by the red, pink and green boxes. In each case the object is released from the front nearside position. If the centre O of the turning circle was inside the car, then it would also be possible for the object to strike the front window.
Note that the impact position does not depend on the speed of the vehicle (and object). 
A: You can think of this in terms of Newton's Laws. Since objects will stay in motion or rest until a force is applied, the object will move forward. However, to analyze where the box will end up, you need to consider the dimensions of the car and how fast it is turning. With these two, you can calculate how far back the object will go or if it hits the back first.
