An automobile driver puts on the brakes and decelerates from 30.0 m/s to 0 in 10.0 s. What distance does the car travel?
(Average speed) x (time) = 15 m/s * 10 s = ___ m
To find the distance the car travels, we can use the formula:
distance = initial velocity * time + (1/2) * acceleration * time^2
First, let's calculate the acceleration:
acceleration = (final velocity - initial velocity) / time
acceleration = (0 - 30.0 m/s) / 10.0 s
acceleration = -3.0 m/s^2
Now, we can substitute the values into the distance formula:
distance = 30.0 m/s * 10.0 s + (1/2) * (-3.0 m/s^2) * (10.0 s)^2
distance = 300.0 m + (-15.0 m/s^2) * 100.0 s^2
distance = 300.0 m - 1500.0 m
distance = -1200.0 m
Since we are only interested in the magnitude of the distance traveled, the car travels a distance of 1200.0 meters.
To find the distance the car travels, we can use the formula:
distance = initial velocity × time + 0.5 × acceleration × time²
In this case, the initial velocity (v₀) is 30.0 m/s, the final velocity (v) is 0 m/s, and the time (t) is 10.0 s. The acceleration (a) can be calculated using the equation:
acceleration = (final velocity - initial velocity) / time
Let's calculate the acceleration first:
a = (0 m/s - 30.0 m/s) / 10.0 s
a = -3.0 m/s² (negative sign indicates deceleration)
Now we can substitute the values into the distance formula:
distance = 30.0 m/s × 10.0 s + 0.5 × (-3.0 m/s²) × (10.0 s)²
Simplifying the equation:
distance = 300.0 m - 0.5 × 3.0 m/s² × 100.0 s²
distance = 300.0 m - 150.0 m
distance = 150.0 m
Therefore, the car travels a distance of 150.0 meters.