Serious vibration when accelerating or holding speed; smooth when coasting

indicates worn cv joints
have the front drive shafts checked by an accredited specialist shop
check for suspension rubbers worn and putting the alignment out under load /acceleration

Take extra caution while performing dirve cycles on public roadways. Drive cycles can be difficult to follow under normal driving conditions. Begin by: - Start the engine. Idle the engine in drive for two and a half minutes with the A/C and rear defroster on. - Turn the A/C and rear defrost off, and accelerate to 55 mph at half throttle. - Hold at a steady speed of 55 mph for three minutes. - Decelerate (coast down) to 20 mph without braking or depressing the clutch. - Accelerate back to 55 to 60 mph at ¾ throttle. - Hold at a steady speed of 55 to 60 mph for five minutes. - Decelerate (coast down) to a stop without braking. If all other emissions systems are functioning properly, completing the drive cycle above will set the "readiness flags" required to pass the smog check. It will not hurt to perform the drive cycle 2 or 3 times before the smog test.

That should still be under a warranty!

Acceleration problem - is it so tough? - Car Forums and Automotive ...

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Once I reach wanted cruising speed of 35 mph or above (and the car ... At that point I keep pressing pedal slowly but car does not accelerate or needs eternity to speed ...Fuel pressure within specs (40 psi in idle) and fuel pressure regulator holds ... "The 3100 V-6 engine is mated to a 4T60E four-speed automatic overdrive ...

It is HVAC 1fuse #39 in the rear fuse block ,this powers the on/off switch for cruise control ! Fuse Block - Rear Beneath the left rear seat. What engine does it have ? 4.2 L or 5.3 l There is no vacuum involved in the operation of the cruise control ! Your vehicle has electronic throttle control .
Cruise control is a speed control system that maintains a desired vehicle speed under normal driving conditions at vehicle speeds above 40 km/h (25 mph). Steep grades may cause variations in the selected vehicle speeds.
The following are the main components of the Cruise Control System:
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The powertrain control module (PCM)

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The On/Off switch

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The Resume/Accel switch

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The Set/Coast switch

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The TCC brake switch

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The stop lamp switch

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The throttle actuator control (TAC) motor

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The vehicle speed sensor

Cruise Control Engaged
The cruise control system will engage and adjust the vehicle speed based on the activation of the following cruise control switches:
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On/Off

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Resume/Accel.

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Set/Coast

The cruise control switches are located on the multifunction/turn signal lever.
The powertrain control module (PCM) monitors the signal circuits of the cruise control switches in order to determine when to capture and maintain the selected vehicle speed. The PCM uses the throttle actuator control (TAC) module motor in order to control the vehicle speed. For further information on the TAC System, refer to Throttle Actuator Control (TAC) System Description in Engine Controls - 4.2 L.
Ignition positive voltage is supplied from the 10 ampere HVAC 1 fuse to the cruise control switch via the ignition 3 voltage circuit. When the normally open cruise control On/Off switch is turned On, the switch closes and the PCM detects a high signal voltage on the cruise control on switch signal circuit. When the normally open Set/Coast switch is pressed, the switch closes and the PCM detects a high signal voltage on the cruise control set/coast switch signal circuit. To engage the cruise control system, turn the On/Off switch On and momentarily press the Set/Coast switch. The PCM will confirm that the cruise control enable criteria has been achieved. The PCM will engage the cruise control system and record the selected vehicle speed. The PCM sends a class 2 message to the instrument panel cluster in order to illuminate the cruise control indicator. Pressing the accelerator pedal, while the cruise control system is engaged, will allow the driver to override the cruise control system in order to accelerate the vehicle beyond the current set vehicle speed. When the accelerator pedal is released, the vehicle will decelerate and resume the current set vehicle speed. The driver can also override the current set vehicle speed via the Set/Coast switch and the Resume/Accel switch. When the cruise control system is engaged, pressing and holding the Set/Coast switch will allow the vehicle to decelerate from the current set vehicle speed without deactivating the cruise control system. When the Set/Coast switch is released, the PCM will record the vehicle speed and maintain the vehicle speed as the new set vehicle speed. When the cruise control system is engaged, momentarily pressing the Set/Coast switch will allow the vehicle to decelerate at 1.6 km/h (1 mph) increments for each time that the Set/Coast is momentarily pressed, with a minimum vehicle speed of 37 km/h (23 mph). When the normally open Resume/Accel switch is activated, the switch closes and the PCM detects a high signal voltage on the cruise control resume/accel switch signal circuit. Activating and holding the Resume/Accel switch, when the cruise control system is engaged, will allow the vehicle to accelerate to a greater vehicle speed than the current set vehicle speed. When the Resume/Accel switch is released, the PCM will record the vehicle speed and maintain the vehicle speed as the new set vehicle speed. When the cruise control system is engaged, momentarily activating the Resume/Accel switch will allow the vehicle to accelerate at 1.6 km/h (1 mph) increments for each time that the Resume/Accel switch is momentarily activated, with the maximum acceleration total of 16 km/h (10 mph) over the current set vehicle speed . Momentarily activating the Resume/Accel switch, after the cruise control system has been disengaged by pressing the brake pedal, will recall the previous set vehicle speed that is recorded in the PCM.

you could have a misfire occurring at this speed only, also you could have a cv joint that is bad that is showing up under acceleration in speed area. another possibility could be wheel balance or a balance weight has come off of a drum or rotor.

I had a similar noise. It turned out to be one of the motor mounts (broken).

Generally... There is ON/OFF - SET - ACCELERATE/RESUME, COAST/DECELERATE. Cruise is available at speeds above 35mph or so. Sometimes there is no main on/off. Cruise on a turn signal stem has a button that pushes in on the end, push when at desired speed. resume/accelerate slides to right, is spring loaded and return left when released. the same lever when slid left is coast/decelerate. Momentarily sliding accelerate and releasing increases crusing speed by a couple mph. If brakes are used cruise disengages, sliding resume returns you to cruise speed after braking. Coast/decelerate disengages cruise, when at desired lower speed hit set. On some, hitting set not needed, when coast is released speed is maintained. Variations may be up/ down instead or may be steering wheel face mounted. Please rate answer. Duct tape is like the force, it has a dark side.. a light side.. and holds the universe together!

maybe a U joint or a bearing

Welcome to fixya the best thing to do is check the rims for imperfections and slight bents that causes the vibrations at that speed go to www.collisionrepairadvice.com to get a wheel repair company to look at.

check out harmonic balancer .