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A 1050 kg sports car is moving westbound at 15.0 m/s on a level road when it collides with a 6320 kg truck driving east on the same road at 14.0 m/s . the two vehicles remain locked together after the collision.

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BlueSky06
In this item, it is assumed that what is being asked is the final velocity and direction after collision. This can be answered through the conservation of momentum. 
 
Momentum is the product of the mass and the velocity,
                               M = m x v
If we take east as positive then, west would be negative.
Through the conservation,
 
                    (1050)(-15 m/s) + (6320 kg)(14 m/s) = (1050 + 6320) x v

The value of v from the equation is 9.87 m/s. Since it is positive, the direction is east. 

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