how long in seconds does it take for a car to accelerate from 0 to 100 km/h2 if acceleration is 10 m/s2?
a = (Vf - Vi)/t
Vf = final velocity
Vi = initial velocity
t = change in time
Make sure you have matching units.
To find out how long it takes for a car to accelerate from 0 to 100 km/h, you need to convert the given acceleration from meters per second squared (m/s^2) to kilometers per hour squared (km/h^2) and then use the formula for time with constant acceleration. Here's a step-by-step explanation of how to solve this problem:
1. Convert the acceleration from meters per second squared (m/s^2) to kilometers per hour squared (km/h^2).
- Since 1 m/s^2 = 3.6 km/h^2, you can multiply the given acceleration of 10 m/s^2 by 3.6 to get the equivalent acceleration in km/h^2.
- So, the acceleration is 10 m/s^2 * 3.6 km/h^2/m/s^2 = 36 km/h^2.
2. Now, let's use the formula for time with constant acceleration:
- The formula is t = √(2d/a), where t is the time, d is the displacement, and a is the acceleration.
- In this case, the displacement is the change in velocity, which is 100 km/h - 0 km/h = 100 km/h.
- So, the formula becomes t = √(2 * 100 km/h / 36 km/h^2).
3. Simplify and calculate:
- Calculate 2 * 100 km/h = 200 km/h.
- Divide 200 km/h by 36 km/h^2 to get approximately 5.56.
- Finally, take the square root (√) of 5.56 to find the time.
Therefore, it takes approximately 5.56 seconds for the car to accelerate from 0 to 100 km/h if the acceleration is 10 m/s^2.