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?
*Cringe*🤮
To find the acceleration of a car, we can use the formula:
Acceleration (a) = (Change in velocity) / (Time taken)
Given that the car goes from 20 to 30 km/h in 1.5 seconds, we can calculate the acceleration.
First, we need to find the "change in velocity" by subtracting the initial velocity from the final velocity:
Change in velocity = Final velocity - Initial velocity
= 30 km/h - 20 km/h
= 10 km/h
Next, we convert the time from seconds to hours since the velocities are given in kilometers per hour:
Time taken = 1.5 seconds = 1.5 / 3600 hours (1 hour = 3600 seconds)
Now, we can plug these values into the acceleration formula:
Acceleration (a) = (Change in velocity) / (Time taken)
= 10 km/h / (1.5 / 3600 hours)
= 10 km/h × (3600 / 1.5) hours
= 10 km/h × 2400 hours
= 24,000 km/h²
Therefore, the acceleration of the car is 24,000 km/h².
Now, to determine how long it will take the car to go from 30 to 36 km/h at the same acceleration, we can use the same formula.
Change in velocity = 36 km/h - 30 km/h = 6 km/h
Acceleration = 24,000 km/h² (as calculated above)
To find the time taken:
Time taken = (Change in velocity) / (Acceleration)
= 6 km/h / 24,000 km/h²
= 6 km/h × (1 / 24,000) h²
= 6 km/h × 0.00004167 h²
≈ 0.00025 hours
Converting the time to seconds:
0.00025 hours = 0.00025 × 3600 seconds/hour
≈ 0.9 seconds
Therefore, at the same acceleration, it will take the car approximately 0.9 seconds to go from 30 to 36 km/h.
a = ∆v/∆t = (10/1.5) km/hr/s
36-30 = (30-20) * 6/10
so, it will take 6/10 as long to make that change