A top fuel dragster can complete a quarter-mile (402 meters) in 4.7 seconds. Assuming that the vehicle starts from rest and that acceleration is constant, calculate (a) the acceleration and (b) the final speed of the top fuel dragster.
the average speed (S) is ... 402 m / 4.7 s
from a zero start, with constant acceleration, the top speed is twice the average
... St = 2 S
acceleration is top speed divided by time
... a = St / 4.7 s
average speed = 402/4.7 = 85.5 m/s
top speed = 2*85.5 = 171 m/s
a = (171-0)/4.7 = 36.4 m/s^2
To calculate the acceleration and final speed of the top fuel dragster, we can use the following formulas:
(a) Acceleration (a) = (Change in Velocity) / (Time)
(b) Final Speed (v) = Initial Speed + (Acceleration * Time)
Given:
Distance (d) = 402 meters
Time (t) = 4.7 seconds
Initial Speed (u) = 0 m/s (since the vehicle starts from rest)
(a) To find the acceleration:
Acceleration (a) = (Change in Velocity) / (Time)
The Change in Velocity (Δv) can be calculated using the formula: Δv = d - u
Δv = d - u
Δv = 402 m/s - 0 m/s
Δv = 402 m/s
Now, we can substitute the values into the first formula to calculate the acceleration:
Acceleration (a) = (Change in Velocity) / (Time)
a = Δv / t
a = 402 m/s / 4.7 s
a ≈ 85.53 m/s²
Therefore, the acceleration of the top fuel dragster is approximately 85.53 m/s².
(b) To find the final speed:
Final Speed (v) = Initial Speed + (Acceleration * Time)
By substituting the given values into the second formula, we can determine the final speed:
v = u + (a * t)
v = 0 m/s + (85.53 m/s² * 4.7 s)
v ≈ 402.291 m/s
Therefore, the final speed of the top fuel dragster is approximately 402.291 m/s.