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A car starts from rest and moves along the path OAB as shown. It moves with a speed of 35 mph along OA and 50 mph along AB. Which is true for the motion of the car during its journey along OAB? The velocity of the car changes due to the change in speed and direction; The change in direction alone causes the velocity of the car to vary; The change in speed alone causes the velocity of the car to vary

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To determine which statement is true regarding the motion of the car along the path OAB, we need to analyze the components that affect velocity.

  1. The velocity of the car changes due to the change in speed and direction.
    This statement is true because the car has two segments of motion with different speeds (35 mph along OA and 50 mph along AB). In addition to changing speed, the car also changes its direction when it moves from OA to AB. Since velocity is a vector quantity that depends on both speed and direction, any change in either one will result in a change in velocity.

  2. The change in direction alone causes the velocity of the car to vary.
    This statement is false. While a change in direction does affect velocity, in this scenario, the car also changes speed. Thus, the variation in velocity cannot be attributed solely to the change in direction.

  3. The change in speed alone causes the velocity of the car to vary.
    This statement is also false when considering the entire journey. Although the speed changes, the velocity's change is due to both speed and direction. Therefore, the change in speed alone does not account for all variations in velocity along the trajectory.

In conclusion, the correct statement about the motion of the car during its journey along OAB is:

The velocity of the car changes due to the change in speed and direction.