When a car is 100 meters from its starting position traveling at 60.0 m/s., it starts braking and comes to a stop 350 meters from its starting position in 8.3 s.
d = 350 100 = 250 m. = Braking distance.
a=(V^2-Vo^3)/2d=(0-60^2)/500=-7.2 m/s^2
To find the car's initial velocity, we can use the equation of motion:
Final velocity = Initial velocity + (Acceleration * Time)
In this case, the final velocity is 0 m/s, since the car comes to a stop. The time is given as 8.3 seconds. So, the equation becomes:
0 = Initial velocity + (Acceleration * 8.3)
To find the acceleration, we can use another equation of motion:
Final position = Initial position + (Initial velocity * Time) + (0.5 * Acceleration * Time^2)
The initial position is 100 meters, the final position is 350 meters, and the time is again 8.3 seconds. We can rearrange the equation to solve for acceleration:
Acceleration = (Final position - Initial position - (Initial velocity * Time))/(0.5 * Time^2)
Now we have both the initial velocity and the acceleration.
To calculate the initial velocity:
0 = Initial velocity + (Acceleration * 8.3)
Solving for the initial velocity:
Initial velocity = - (Acceleration * 8.3)
Now, we can substitute the values into the equation:
Initial velocity = - (4.818 * 8.3) [using the given acceleration]
Initial velocity = - 40.01 m/s
Therefore, the car's initial velocity is -40.01 m/s. The negative sign indicates that the car is moving in the opposite direction of the initial position.