96Tbird strange shifting/acceleration

i bought a 96 tbird 4,6l automatic.
a had a very hard shifting and a DTC of failing engine speed sensor at transm.
a accelerate from 00MPH-50MPH. when the 50MPH were reached the car shifted up and down in a strange behaviour. then a stopped the car.
i restarted the car and since the a have a strange behaviour from 0-15MPHcar accelerates normal from 15-20MPH the RPM is rising very high and speed is increasing very very slowly. when 20MPH are reached car shifts and it is normal..

 

I had something similar happen to me in my 97 thunderbird. Fortunately I was stopped and had my breaks on, the rpms went crazy and my rear tires started spinning

 

Thanks for the First answer. And the quotation ur First answer. This has helped me a lot!