What is the acceleration of a car that goes from 20 to 30 km/h in 1.5s? At the same acceleration, how long will it take the car to go from 30 to 36 km/h?
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To determine the acceleration of a car, you'll need to use the equation:
acceleration = change in velocity / time
In this case, the change in velocity is from 20 km/h to 30 km/h, which corresponds to a difference of 10 km/h. However, it's important to convert the velocities to m/s, as the SI unit for acceleration is meters per second squared (m/s^2). To convert km/h to m/s, divide by 3.6:
20 km/h = (20/3.6) m/s = 5.56 m/s
30 km/h = (30/3.6) m/s = 8.33 m/s
Next, subtract the initial velocity from the final velocity to find the change in velocity:
change in velocity = 8.33 m/s - 5.56 m/s = 2.77 m/s
Finally, divide the change in velocity by the time taken to get the acceleration:
acceleration = 2.77 m/s / 1.5 s = 1.85 m/s^2
Thus, the acceleration of the car is 1.85 m/s^2.
To find out how long it will take for the car to go from 30 km/h to 36 km/h with the same acceleration, you'll use the same equation:
acceleration = change in velocity / time
This time, the change in velocity is from 30 km/h to 36 km/h, which is a difference of 6 km/h. Again, convert the velocities to m/s:
30 km/h = (30/3.6) m/s = 8.33 m/s
36 km/h = (36/3.6) m/s = 10 m/s
Subtracting the initial velocity from the final velocity gives the change in velocity:
change in velocity = 10 m/s - 8.33 m/s = 1.67 m/s
Now, you can rearrange the formula to solve for time:
time = change in velocity / acceleration
Plug in the values:
time = 1.67 m/s / 1.85 m/s^2 ≈ 0.903 s
Therefore, it will take approximately 0.903 seconds for the car to go from 30 km/h to 36 km/h with the same acceleration.
a = (30 - 20) km/h / 1.5 s
t = (36 - 30) km/h / a