A car initially traveling northeast (45° N of E) at 28.3 m/s takes 6.0 s to turn to the east. After the turn, the car is traveling due east at 20.0 m/s. What is the value and direction of the change in velocity?

change in velocity= finalvelocity-initialvelocity

breakthe initial velocity into N,E components.

Vi=28.3*.707N+28.3*.707E
Vf=20 E

subtract. change in velocity=Vf-Vi

thank you

To find the change in velocity, we need to subtract the initial velocity from the final velocity. Let's break it down step by step:

Step 1: Decompose the initial velocity into north and east components.
The initial velocity is given as 28.3 m/s at 45° N of E. We need to find the north and east components of this velocity.

The north component = initial velocity × sine(angle)
North component = 28.3 m/s × sin(45°) ≈ 20.04 m/s (rounded to two decimal places)

The east component = initial velocity × cosine(angle)
East component = 28.3 m/s × cos(45°) ≈ 20.04 m/s (rounded to two decimal places)

So, the initial velocity can be broken down into 20.04 m/s north and 20.04 m/s east components.

Step 2: Find the change in velocity in the north and east direction.
The change in velocity in the north direction will be zero because the car does not change its direction in the north-south axis.

Change in velocity in the north direction = 0 m/s

The change in velocity in the east direction can be found by subtracting the initial east component from the final east component.

Change in velocity in the east direction = Final east component - Initial east component
Change in velocity in the east direction = 20.0 m/s - 20.04 m/s ≈ -0.04 m/s (rounded to two decimal places)

So, the change in velocity in the east direction is approximately -0.04 m/s.

Step 3: Find the magnitude and direction of the change in velocity.
To find the magnitude of the change in velocity, use the Pythagorean theorem.

Magnitude of the change in velocity = sqrt((change in velocity in the north direction)^2 + (change in velocity in the east direction)^2)
Magnitude of the change in velocity = sqrt((0 m/s)^2 + (-0.04 m/s)^2) ≈ 0.04 m/s (rounded to two decimal places)

So, the magnitude of the change in velocity is approximately 0.04 m/s.

The direction of the change in velocity can be found using the inverse tangent function.

Direction = arctan(change in velocity in the north direction / change in velocity in the east direction)
Direction = arctan(0 m/s / -0.04 m/s) ≈ 90°

Since arctan(0) is equal to 0, we would normally divide by 0. However, in this case, we are dividing zero by a small negative number approaching zero. As the value approaches zero, the direction approaches 90°.

Therefore, the direction of the change in velocity is approximately 90°, or due east.

In summary, the change in velocity is approximately 0.04 m/s in the east direction.