A car traveling at 22.0 m/s accelerates for 2.47 seconds at a rate of 2.25 m/s2. How far will it travel in meters during this time?
s = vt + 1/2 at^2
so plug in your numbers
d = 1/2 a t^2 + v t = (1/2 * 2.25 * 2.47^2) + (22.0 * 2.47)
To find the distance the car will travel, we can use the equation:
distance = initial velocity * time + 0.5 * acceleration * time^2
Given:
- Initial velocity (u) = 22.0 m/s
- Time (t) = 2.47 seconds
- Acceleration (a) = 2.25 m/s^2
Plugging these values into the equation, we get:
distance = (22.0 m/s) * (2.47 s) + 0.5 * (2.25 m/s^2) * (2.47 s)^2
First, we solve for the term (u * t):
(22.0 m/s) * (2.47 s) = 54.34 m
Next, we solve for the term (0.5 * a * t^2):
0.5 * (2.25 m/s^2) * (2.47 s)^2 ≈ 6.50 m
Finally, we add the two terms together to find the total distance:
distance = 54.34 m + 6.50 m = 60.84 m
Therefore, the car will travel approximately 60.84 meters during this time.