Final answer:
OPTION D.The change in velocity of the car is 31 m/s at an angle, as velocity is a vector and the car's direction changes while its speed remains constant. The change in velocity is calculated using the Pythagorean theorem.
Step-by-step explanation:
The question asks about the change in velocity of a car that travels first due east at 22 m/s and then turns to travel due south at 22 m/s. Velocity is a vector quantity which means it has both a magnitude and a direction. Since the direction of the car's motion changes while the speed (magnitude of the velocity) remains constant, there is indeed a change in velocity.
To find the change in velocity, you would subtract the initial velocity vector from the final velocity vector. This can be represented by a right-angled triangle with the sides representing the eastward and southward velocity components, both having magnitude of 22 m/s. Using the Pythagorean theorem, the magnitude of the change in velocity (the hypotenuse of the triangle) is √(22^2 + 22^2) m/s, which equals 31 m/s at a 45-degree angle from the original direction (due southeast).
Therefore, the correct answer to the student's question is d) 31 m/s at an angle.