Answer:
5 m/s due West
Step-by-step explanation:
(a) The change in speed of the car can be found using the Pythagorean theorem, which states that the square of the hypotenuse of a right triangle is equal to the sum of the squares of the other two sides. In this case, the change in speed is the magnitude of the change in velocity, and is given by:
change in speed = sqrt((25 m/s)^2 + (30 m/s)^2) = 39.05 m/s (rounded to two decimal places)
Therefore, the change in speed of the car is approximately 39.05 m/s.
(b) The change in velocity of the car can be found by subtracting the initial velocity from the final velocity. The initial velocity was 30 m/s due East, and the final velocity was 25 m/s due South. To subtract these velocities, we need to use vector subtraction. This involves breaking the velocities into their x and y components and subtracting the components separately. The x component of the initial velocity is 30 m/s, and the x component of the final velocity is 0 m/s. The y component of the initial velocity is 0 m/s, and the y component of the final velocity is -25 m/s. Therefore, the change in velocity of the car is:
change in velocity = final velocity - initial velocity = (-30 m/s) - (-25 m/s) = -5 m/s due West
Therefore, the change in velocity of the car is 5 m/s due West.