A car moving with a constant acceleration covers the distance between two points 80 m apart in 8.0 s. Its velocity as it passes the second point is 14 m/s.How far behind the first point was the car at rest?
To solve this problem, we need to break it down into steps:
Step 1: Identify the given information.
We are given:
- Distance between two points: 80 m
- Time taken to cover the distance: 8.0 s
- Velocity at the second point: 14 m/s
Step 2: Find the acceleration of the car.
We know that acceleration (a) is the rate of change of velocity. Since the car is moving with constant acceleration, we can find it using the formula:
acceleration (a) = change in velocity / time
The change in velocity can be calculated by subtracting the initial velocity (0 m/s) from the final velocity (14 m/s):
Change in velocity = 14 m/s - 0 m/s = 14 m/s
Now, we can find the acceleration:
acceleration = change in velocity / time = 14 m/s / 8.0 s = 1.75 m/s²
Step 3: Find the distance the car was behind the first point when it was at rest.
To find the distance the car was behind the first point when it was at rest, we need to determine the initial velocity and the time it took to reach the second point.
Given that the car started from rest, the initial velocity (u) is 0 m/s. We also know the time it took to cover the distance between the two points is 8.0 s.
Now, we can use the equation of motion:
distance (s) = initial velocity (u) * time (t) + 0.5 * acceleration (a) * time (t)²
Using the known values:
80 m = 0 m/s * 8.0 s + 0.5 * 1.75 m/s² * (8.0 s)²
Simplifying the equation:
80 m = 0 m + 0.5 * 1.75 m/s² * 64 s²
80 m = 56 m
Therefore, the car was 80 m - 56 m = 24 m behind the first point when it was at rest.