To find the time it takes for the car to travel a certain distance with a given acceleration, you can use the following kinematic equation:
d=12at2d = frac{1}{2}at^2d=21at2
where:
- ddd is the distance traveled (200 m in this case),
- aaa is the acceleration (10 m/s² in this case),
- ttt is the time it takes.
Plugging in the values we have:
200=12×10×t2200 = frac{1}{2} imes 10 imes t^2200=21×10×t2
Simplifying the equation:
200=5t2200 = 5t^2200=5t2
Dividing both sides of the equation by 5:
t2=40t^2 = 40t2=40
Taking the square root of both sides to solve for ttt:
t=40≈6.32 st = sqrt{40} approx 6.32 ext{s}t=40≈6.32 s
Therefore, it takes the car approximately 6.32 seconds to travel 200 meters with an acceleration of 10 m/s².