transmission cable on 1991 volvo 740 problems and remedie

My 1991 Volvo 740 will accelerate just fine as long as I press on the gas softly. When I need to accelerate quickly and step on the gas hard, the car slows down. It's the damndest thing. When I'm climbing a steep incline it slows to 30-40 mph while folks around me are doing 60-75 mph. What is wrong with my car. I've changed the mass air flow sensor, and the gas filter. One mechanic says it's the transmission. I don't believe it. The car changes gears fine with slow acceleration. What is wrong with my car?

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Slow rolling daddy.
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