A 873-kg (1930-lb) dragster, starting from rest completes a 403.6-m (0.2523-mile) run in 4.935 s. If the car had a constant acceleration, what would be its acceleration and final velocity?
Well, well, well, we have ourselves a speedy dragster! Let's calculate its acceleration and final velocity, shall we?
To find the acceleration, we'll use the equation: acceleration = (change in velocity) / time.
Now, the dragster starts from rest, so its initial velocity is zero. The final velocity can be found using the formula: final velocity = initial velocity + (acceleration * time). Since initial velocity is zero, we can simplify this to: final velocity = acceleration * time.
Let's plug in the numbers, my friend! The distance is 403.6 meters, and the time is 4.935 seconds. Let's convert the mass to kilograms, which gives us 873 kg.
Acceleration = (403.6 m) / (4.935 s)
Acceleration = 81.8 m/s² (approximately)
Final velocity = 81.8 m/s² x 4.935 s
Final velocity = 403.3 m/s (approximately)
So there you have it! The dragster's acceleration is approximately 81.8 m/s², and its final velocity is around 403.3 m/s. That's one fast dragster! Beep beep!
To find the acceleration and final velocity of the dragster, we can use the equations of motion.
1. First, convert the weight of the dragster from pounds to kilograms:
1930 lb = 1930 lb × 0.4536 kg/lb = 875.908 kg (rounded to 3 decimal places)
2. The initial velocity (u) of the dragster is 0 m/s since it starts from rest.
3. The distance traveled (s) is given as 403.6 m.
4. The time taken (t) is given as 4.935 s.
5. Let's use the equation:
s = ut + (1/2)at^2
6. Rearranging the equation, we get:
a = (2s - 2ut) / t^2
7. Substituting the values into the equation:
a = (2 × 403.6 m - 2 × 0 m/s × 4.935 s) / (4.935 s)^2
8. Evaluating the equation, we find:
a = 81.976 m/s^2 (rounded to 3 decimal places)
9. To find the final velocity (v), we can use the equation:
v = u + at
10. Substituting the values into the equation:
v = 0 m/s + 81.976 m/s^2 × 4.935 s
11. Evaluating the equation, we find:
v = 404.083 m/s (rounded to 3 decimal places)
Therefore, the dragster has an acceleration of 81.976 m/s^2 and a final velocity of 404.083 m/s.
To find the acceleration and final velocity of the dragster, we can use the kinematic equation:
\[d = v_0t + \frac{1}{2}at^2\]
Where:
d = distance traveled (403.6 m)
\(v_0\) = initial velocity (0 m/s, since the car starts from rest)
t = time taken (4.935 s)
a = acceleration (unknown)
Rearranging the equation to solve for acceleration (a):
\[a = \frac{2(d - v_0t)}{t^2}\]
Using the known values, we can substitute them into the equation:
\[a = \frac{2(403.6 - 0 \cdot 4.935)}{(4.935)^2}\]
Calculating the numerator:
\[2(403.6 - 0) = 807.2\]
Calculating the denominator:
\((4.935)^2 = 24.355225\)
Now, substituting the values back into the equation to solve for acceleration:
\[a = \frac{807.2}{24.355225}\]
Calculating the equation:
\[a ≈ 33.10 \, \text{m/s}^2\]
So, the acceleration of the dragster is approximately 33.10 m/s².
To find the final velocity (v) of the dragster, we can use another kinematic equation:
\[v = v_0 + at\]
Since the initial velocity (v₀) is 0 m/s, we can simplify the equation:
\[v = at\]
Substituting the known values:
\[v = 33.10 \cdot 4.935\]
Calculating the equation:
\[v ≈ 163.14 \, \text{m/s}\]
Therefore, the dragster's acceleration is approximately 33.10 m/s², and its final velocity is approximately 163.14 m/s.
avg velocity=403.6/time
final velocity=2*avg velocity
a= (vf=vi)/time= 2*403.6/4.935^2
vf above.