To determine the time needed for the car to travel a distance of 25 meters, we can use the equation of motion for constant acceleration:
s = v0t+ (1/2)* a*t^2
Where:
s is the distance traveled, v0 is the initial velocity, t is the time taken, and a is the acceleration.
In this case, the initial velocity (v0) is given as 20 m/s. The acceleration (a) is given as 0.8s m/s^2.
To find the time taken (t), we substitute the given values into the equation and solve for t:
2520* t + (1/2)* 0.8*t^2
Simplifying the equation:
25 = 20t + 0.4t ^ 2
Rearranging the equation:
0.4t ^ 2 + 20t - 25 = 0
Now we can solve this quadratic equation using the quadratic formula:
t = (- b plus/minus sqrt(b ^ 2 - 4ac)) / (2a)
For this equation, a = 0.4 b = 20 and c = - 25
Plugging in these values into the quadratic formula:
t = (-20 ± √(20^2-4 0.4-25)) / (2 * 0.4)
For this equation, a = 0.4 b = 20 and c = - 25
Plugging in these values into the quadratic formula:
t = (-20 ± √(20^2-4*0.4* -25)) / (2 * 0.4)
Simplifying:
t = (- 20 plus/minus sqrt(400 + 40)) / 0.8 t = (-20 ± √440) / 0.8
Now we can calculate the time by evaluating the two possible solutions:
t = (- 20 + sqrt(440)) / 0.8
t = 2.275 seconds
t = (-20-440) / 0.8
t=-32.275 seconds (extraneous solution, as time cannot be negative)
Therefore, the time needed for the car to travel a distance of 25 meters is approximately 2.275 seconds.