A 873 kg (1930 lb) dragster completed the 402.0 m (0.2498 mile) run in 4.950 s. If the car has constant acceleration, what would be its acceleration and final velocity?
To find the acceleration and final velocity, we can use the kinematic equations of motion. Here's how:
Step 1: Convert the given mass from pounds to kilograms:
Given mass = 1930 lb
1 lb = 0.4536 kg
Mass = 1930 lb × 0.4536 kg/lb ≈ 876.5 kg
Step 2: Convert the distance from miles to meters:
Given distance = 0.2498 mile
1 mile = 1609.34 meters
Distance = 0.2498 mile × 1609.34 meters/mile ≈ 401.7 meters
Step 3: Use the formula v = u + at to find the acceleration:
Initial velocity (u) = 0 m/s (assuming the dragster starts from rest)
Final velocity (v) = unknown
Time (t) = 4.950 s
v = u + at
v = 0 + A × 4.950 (where A is the acceleration)
v = 4.950A
Step 4: Use the formula s = ut + 0.5at^2 to find the acceleration:
Here, s is the distance traveled.
s = ut + 0.5at^2
401.7 = 0 × 4.950 + 0.5A × (4.950)^2
401.7 = 12.252A
A = 401.7 / 12.252
A ≈ 32.8 m/s^2
So, the acceleration of the dragster is approximately 32.8 m/s^2.
Step 5: Substitute the value of acceleration (A) into the previously derived formula v = 4.950A to find the final velocity (v):
v = 4.950A
v = 4.950 × 32.8
v ≈ 162 m/s
Therefore, the final velocity of the dragster is approximately 162 m/s.