A roller coaster cart travelling due north at 20m/s that turns left during an interval of 4.0s without changing speed. Find the average acceleration.
I understand the mathematics behind it (using pythagoras's theorem to find velocity and the formula acceleration = velocity/time) BUT I don't understand how to find the direction.
The answer in my text book says south west, but intuitively that just doesn't make sense if you draw out the path taken. Can anyone explain how the direction is south west?
Draw a vector from the origin pointing
due north. Then draw a vector from the
origin pointing due west. Since the 2 vectors are equal, the resultant vector
will fall midway between them(135o or
North West). Mathematically:
tanAr = Y/X = 20/-20 = -1.0
Ar = -45o = Reference angle.
A = -45 + 180 = 135o, North West.
If we change the North bound vector to due South, then the direction would
be South West.
To understand the direction of the average acceleration, let's break it down step by step.
First, consider the initial velocity of the roller coaster cart, which is due north at 20 m/s. Since the cart is initially travelling north and then turns left, we can assume that the left turn is in the west direction.
During the 4.0s interval, the cart changes its direction and continues moving at 20 m/s. So, the displacement of the cart during this interval can be represented as a vector going west.
Now, let's consider the average acceleration. Average acceleration is defined as the change in velocity divided by the time taken. In this case, the velocity does not change, so the change in velocity is zero.
To find the direction of the average acceleration, we need to consider the relationship between velocity and acceleration. If the velocity and acceleration vectors are in the same direction, the speed of the object increases. If they are in opposite directions, the speed decreases.
In this scenario, the velocity vector is initially due north, while the acceleration vector is zero (since there is no change in velocity). So, the velocity and acceleration vectors are in opposite directions, meaning the speed remains the same. This indicates that there is deceleration or negative acceleration in the direction opposite to the initial velocity.
Since the initial velocity was due north, the average acceleration's direction will be opposite, which is due south. Additionally, since the cart changes its direction while turning left, we can say that the direction is also toward the west. Therefore, the average acceleration can be described as south-west.
It is important to note that the average acceleration direction is not based on the path taken but on the change in velocity over the given time interval.