A drag racer accelerated from 0 to 475km/h in 4.88 s. Assuming a constant acceleration, how far did it travel?
The average speed was 237.5 km/h (half the maximum, at the end). Convert that average speed to m/s and multiply the result by 4.88 s
237.5 km/h = 65.97 m/s
Take it from there.
Well, let me do some quick calculations while trying not to get too dizzy! Hold on tight!
If we assume constant acceleration, we can use the equation:
distance = (initial velocity * time) + (0.5 * acceleration * time^2)
Since the initial velocity is 0, and we have the time of 4.88 seconds, we just need to find the acceleration.
Using the equation:
final velocity = initial velocity + (acceleration * time)
We can rearrange it to calculate the acceleration:
acceleration = (final velocity - initial velocity) / time
Let me plug in the numbers and hold onto my clown wig!
acceleration = (475 km/h - 0 km/h) / 4.88 s
acceleration = 97.34 km/h / s
Alright, let's calculate the distance now:
distance = (0 * 4.88) + (0.5 * 97.34 * (4.88^2))
distance = 0 + (0.5 * 97.34 * 23.78)
distance = 0 + 1122.4184
distance ≈ 1122.4 meters
So, this drag racer traveled approximately 1122.4 meters at the end of 4.88 seconds! That's a lot of ground covered in a short time!
To find the distance traveled by the drag racer, we can use the equation:
Distance = (Initial Velocity x Time) + (0.5 x Acceleration x Time^2)
In this case, the initial velocity is 0 km/h (since the drag racer starts from rest).
The acceleration can be calculated using the formula:
Acceleration = (Final Velocity - Initial Velocity) / Time
Final Velocity = 475 km/h
Time = 4.88 s
Substituting these values into the formula, we have:
Acceleration = (475 - 0) / 4.88
Acceleration = 97.35 km/h/s
Now, we can substitute the values of initial velocity, time, and acceleration into the distance formula:
Distance = (0 x 4.88) + (0.5 x 97.35 x 4.88^2)
Calculating further:
Distance = 0 + (0.5 x 97.35 x 4.88^2)
Distance = 0 + (0.5 x 97.35 x 23.8144)
Distance = 0 + 11520.72816
Therefore, the drag racer traveled approximately 11520.72816 km.
To determine the distance traveled by the drag racer, we can use the basic kinematic equation:
d = (1/2) * a * t^2
where:
d is the distance traveled,
a is the acceleration, and
t is the time taken.
First, let's convert the initial speed from km/h to m/s:
475 km/h * (1000 m/1 km) * (1 h/3600 s) = 131.9 m/s
Now, we need to find the acceleration, which is a = Δv / t, where Δv is the change in velocity.
To find Δv, we need to determine the final velocity (vf). Since the initial velocity (vi) is 0 (starting from rest), we can use the equation:
vf = vi + a*t
475 km/h * (1000 m/1 km) * (1 h/3600 s) = 131.9 m/s
vi = 0 m/s
t = 4.88 s
vf = 0 + a * 4.88
131.9 = 4.88a
a = 131.9 / 4.88 ≈ 27.03 m/s^2
Now that we have the acceleration, we can substitute the values into the distance equation:
d = (1/2) * a * t^2
d = (1/2) * 27.03 * (4.88)^2
d ≈ 326.84 meters
Therefore, the drag racer traveled approximately 326.84 meters.