A 873-kg (1930-lb) dragster, starting from rest completes a 403.7-m (0.2523-mile) run in 4.920 s. If the car had a constant acceleration, what would be its acceleration and final velocity?
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V = d / t = 403.7 / 492 = 82.1 m/s.
a = (Vf - Vo) / t,
a = (82.1 - 0) / 4.92 = 16,7 m/s^2.
To find the acceleration of the dragster, we can use the equation:
acceleration (a) = (final velocity - initial velocity) / time
Since the dragster starts from rest (initial velocity is 0), the equation simplifies to:
a = final velocity / time
To find the final velocity, we can use the equation of motion:
final velocity = initial velocity + acceleration * time
Since the dragster starts from rest (initial velocity is 0), the equation simplifies to:
final velocity = acceleration * time
We know the values for the time and distance covered by the dragster:
time (t) = 4.920 s
distance (d) = 403.7 m
Now, let's calculate the acceleration:
a = final velocity / time
To find the final velocity, we need to determine the value of time it takes to cover 403.7 m:
time = 403.7 m / final velocity
The final velocity can be found by substituting acceleration with a:
final velocity = a * time
Now, we have two equations that we can use to solve for acceleration and final velocity. Let's substitute the equation for final velocity into the first equation:
a = (a * time) / time
By canceling out time, we find:
a = a
This equation tells us that the acceleration of the dragster is equal to the acceleration of the dragster, which doesn't provide any useful information. It means that the dragster has a constant acceleration, but we need more information to calculate its value.
Please provide additional data or double-check the given data to proceed with solving for the acceleration and final velocity of the dragster.
To find the acceleration and final velocity of the dragster, we can use the following kinematic equations:
1. vf = vi + at - Equation (1)
2. xf = xi + vit + 1/2at^2 - Equation (2)
Given:
- Mass (m) = 873 kg
- Distance (xf - xi) = 403.7 m
- Time (t) = 4.920 s
- Initial velocity (vi) = 0 m/s (starting from rest)
First, let's find the acceleration (a) using Equation (2). Rearranging the equation, we get:
xf - xi = vit + 1/2at^2
Substituting the given values:
403.7 m = 0(4.920 s) + 1/2 a (4.920 s)^2
403.7 m = 1/2 a (24.204 s^2)
a = (2 * 403.7 m) / (24.204 s^2)
a = 16.689 m/s^2
Therefore, the acceleration of the dragster is 16.689 m/s^2.
Now, let's find the final velocity (vf) using Equation (1). Again, rearranging the equation, we get:
vf = vi + at
Substituting the given values:
vf = 0 + 16.689 m/s^2 * 4.920 s
vf = 82.160 m/s
Therefore, the final velocity of the dragster is 82.160 m/s.
To convert the final velocity to miles per hour (mph), we can use the conversion factor:
1 m/s ≈ 2.237 mph
So, the approximate final velocity in mph would be:
82.160 m/s * 2.237 mph = 183.826 mph
Hence, the acceleration of the dragster is 16.689 m/s^2, and its final velocity is approximately 183.826 mph.