A car moving at a constant speed of 50km/h turns a corner, changing it's direction from north to west. What is it's change in velocity. What was the acceleration if the then took 5s
To calculate the change in velocity, we need to determine the magnitude and direction of the change.
The car is initially moving in the north direction and then turns to the west direction. The change can be represented as a vector pointing from north to west.
We can break the change in velocity into its north and west components. The magnitude of the northward component remains the same, which is 50 km/h. The magnitude of the westward component also remains the same.
Thus, the change in velocity can be calculated using the Pythagorean theorem:
Change in velocity = sqrt((50 km/h)^2 + (50 km/h)^2)
Change in velocity = sqrt(2(50 km/h)^2)
Change in velocity = sqrt(2(2500 km^2/h^2))
Change in velocity = sqrt(5000 km^2/h^2)
Change in velocity ≈ 70.7 km/h
So, the change in velocity is approximately 70.7 km/h.
Now, let's calculate the acceleration using the given time:
Acceleration = (Change in velocity) / (Time taken)
Acceleration = (70.7 km/h) / (5 s)
Acceleration ≈ 14.1 km/h/s
Therefore, the acceleration of the car is approximately 14.1 km/h/s.
To find the change in velocity and acceleration, we first need to understand the difference between velocity and acceleration.
Velocity is a vector quantity that describes the rate at which an object changes its position. It is defined by both magnitude (speed) and direction. Acceleration, on the other hand, is the rate of change of velocity over time.
In the given scenario, the car is initially moving north and then turns west. The change in direction indicates a change in velocity. However, the magnitude (speed) remains constant at 50 km/h.
To calculate the change in velocity, we need to determine the vector subtraction of the initial and final velocities. Since the car is turning from north to west, the change in velocity can be calculated by subtracting the initial northward velocity from the final westward velocity.
Since velocity is a vector, we need to consider the direction. In this case, the north direction and west direction are perpendicular to each other, forming a right angle. Therefore, we can use the Pythagorean theorem to find the magnitude of the change in velocity.
To do this, we find the magnitude of the northward velocity using the initial speed of 50 km/h. Then, we find the magnitude of the westward velocity, which is also 50 km/h. Finally, we can find the magnitude of the change in velocity by computing the square root of the sum of the squares of the northward and westward velocities.
Now, let's move on to the acceleration. If the car took 5 seconds to complete the turn, we can use the definition of acceleration, which is the change in velocity divided by the change in time.
To find the acceleration, we divide the magnitude of the change in velocity by the time taken, which is 5 seconds in this case.
In summary:
- The change in velocity can be found by calculating the square root of the sum of the squares of the initial northward velocity and final westward velocity.
- The magnitude of the acceleration can be found by dividing the change in velocity by the time taken.
Please note that the answer will depend on the units used, and make sure to convert them if necessary.