A car engine has a limited range of revolutions that it can achieve. In normal operation this is from around 800 revolutions per minute to 7,000 revolutions per minute. Any higher than this and the engine would suffer damage. So one reason for using a gearbox is to allow the engine to continue transferring power to the wheels over all speeds.
Secondly consider this:
If the engine were set to make the car move at 70 MPH then the amount of torque required to make the car move from a standstill would be greater than the amount of power the car could produce to move the car forward. Moving from a standing start would stall the engine. So its true to say that the gearbox sacrifices speed for torque.
To do this, the gearbox changes the ratio of the engine speed and the wheels. Starting in a low gear the engine spins more revolutions to get one spin of the wheels. In a high gear the ratio of the engine revs to the wheel revs in closer to or above unity.
Cars can have fitted either a manually selected gear box, a semiautomatic or fully automatic gearbox. In a manual select car the ratio is selected via a gear stick and the selections is by the driver. In a semi-select car the clutch is automatic but the gear selection is manual. In a fully automatic the clutch and the gearbox selection is either by a mechanical system or in the case of newer cars via a small computer.
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