A car is traveling at 33.0 m/s when the driver uses the brakes to slow down to 29.0 m/s in 2.50 seconds. How many meters will it travel during that time
a = (29.0 - 33.0)/2.50 = - 1.60 m/s^2
d = Vi t + (1/2)a t^2
d = 33.0(2.50) - 0.800(2.50)^2
To find the distance traveled during 2.50 seconds, we can use the average velocity formula:
Average velocity = (final velocity + initial velocity) / 2
We know the initial velocity is 33.0 m/s, and the final velocity is 29.0 m/s. Plugging these values into the formula, we get:
Average velocity = (29.0 m/s + 33.0 m/s) / 2
Average velocity = 62.0 m/s / 2
Average velocity = 31.0 m/s
Now, we can use the formula for distance traveled with constant acceleration:
Distance = (initial velocity * time) + (1/2 * acceleration * time^2)
Since the car is slowing down, the acceleration is negative. Let's assume the acceleration is constant between the initial and final velocities.
Substituting the given values into the formula:
Distance = (33.0 m/s * 2.50 s) + (1/2 * acceleration * (2.50 s)^2)
To find the acceleration, we can use the formula:
Acceleration = (final velocity - initial velocity) / time
Substituting the given values:
Acceleration = (29.0 m/s - 33.0 m/s) / 2.50 s
Acceleration = -4.0 m/s / 2.50 s
Acceleration = -1.6 m/s^2
Now we can calculate the distance traveled:
Distance = (33.0 m/s * 2.50 s) + (1/2 * -1.6 m/s^2 * (2.50 s)^2)
Distance = 82.5 m - 5.0 m
Distance = 77.5 m
Therefore, the car will travel 77.5 meters during that time.
To find the distance traveled during a certain time interval when the initial and final velocities are known, you can use the average velocity formula.
The average velocity formula is:
Average Velocity (v_avg) = (Initial Velocity (v_i) + Final Velocity (v_f)) / 2
In this case, the initial velocity (v_i) is 33.0 m/s, and the final velocity (v_f) is 29.0 m/s. So, let's plug in these values into the formula:
v_avg = (33.0 m/s + 29.0 m/s) / 2
v_avg = 62.0 m/s / 2
v_avg = 31.0 m/s
Now, we can use the average velocity (v_avg) and the time interval (t = 2.50 s) to find the distance traveled. The formula for distance is:
Distance (d) = Velocity (v) * Time (t)
Plugging in the values:
d = v_avg * t
d = 31.0 m/s * 2.50 s
d = 77.5 m
Therefore, the car will travel 77.5 meters during the 2.50 seconds.