It only takes around an hour and 15 minutes to drive from Newcastle to Worcester depending on traffic. Rush hour is usually between 8am and 9am and from 5pm-6pm. It is only a 70 mile journey so the best way to make the trip is by road or by train. Train tickets can be very cheap of you are booking in advance but if you dont have time to book early then going my car is the most cost effective.
For more information on transportation in the UK you can click the link below:-
http://www.destination360.com/europe/uk/transportation