In your moving car, you covered 2.0 m during the first 1.0 s, 4.0 m during the second 1.0 s, 6.0 m during the third 1.0 s, and so forth.
Find the acceleration.
a = change in v / change in t
t1 = 1 Y1 = 2 V1 = 2 Dv = 2
t2 = 2 Y2 = 6 V2 = 4 Dv = 2
t3 = 3 Y3 = 12V3 = 6 Dv = 2
change in V = 2/1 = 2 m/s^2
To find the acceleration, we need to calculate the change in velocity over time. Since the car is moving in a straight line and the distances covered during each second are increasing by 2.0 m, we can assume that the velocity is changing linearly with time.
The distances covered during each second are:
First second: 2.0 m
Second second: 4.0 m
Third second: 6.0 m
The change in velocity between each second is:
First second: 2.0 m/s
Second second: 4.0 m/s - 2.0 m/s = 2.0 m/s
Third second: 6.0 m/s - 4.0 m/s = 2.0 m/s
Since the change in velocity is constant (2.0 m/s) for each second, we can calculate the average acceleration using the formula:
Average acceleration = change in velocity / time
Let's calculate the average acceleration using the change in velocity during the first second:
Average acceleration = 2.0 m/s / 1.0 s = 2.0 m/s^2
Therefore, the acceleration of the car is 2.0 m/s^2.
To find the acceleration, we can use the formula for acceleration:
acceleration = change in velocity / time
In this case, since the car is moving with a constant acceleration, we can find the change in velocity by subtracting the initial velocity from the final velocity.
First, let's determine the initial and final velocities for each time interval:
- During the first 1.0s, the car covered 2.0m. We can take the final velocity as the velocity after this interval, which is also the initial velocity for the next interval. Therefore, the initial velocity is 0 m/s and the final velocity is 2.0 m/s.
- During the second 1.0s, the car covered 4.0m. Again, the final velocity of this interval will be the initial velocity for the next interval. Therefore, the initial velocity is 2.0 m/s and the final velocity is 6.0 m/s.
- During the third 1.0s, the car covered 6.0m. Once more, we take the final velocity of this interval as the initial velocity for the next. Therefore, the initial velocity is 6.0 m/s and the final velocity is 10.0 m/s.
Now, we can calculate the acceleration for each interval using the formula:
acceleration = (final velocity - initial velocity) / time
- For the first interval: acceleration = (2.0 m/s - 0 m/s) / 1.0 s = 2.0 m/s²
- For the second interval: acceleration = (6.0 m/s - 2.0 m/s) / 1.0 s = 4.0 m/s²
- For the third interval: acceleration = (10.0 m/s - 6.0 m/s) / 1.0 s = 4.0 m/s²
Since the acceleration is constant throughout, we can see that the acceleration is 4.0 m/s².