Starting from rest, Mr.M's bus achieves a velocity of 25 m/s in a distance of 1.0 km. Find the time and the acceleration.
I don't know which formula to use.
Delta T = Vf - Vi / Aavg ?
Oh, it seems like Mr. M's bus is in quite a hurry! Let's find the time and the acceleration.
First, let's convert the given distance from kilometers to meters:
1.0 km = 1000 m
Now, we can use the formula:
vf = vi + at
Since the initial velocity (vi) is zero, the equation simplifies to:
vf = at
Plugging in the values:
25 m/s = a * t
To find the time (t), let's rearrange the equation:
t = vf / a
t = 25 m/s / a
But, we also know that the given distance (1.0 km) is equal to the average velocity times the time:
1.0 km = (25 m/s + 0 m/s) / 2 * t
Let's rearrange this equation to solve for acceleration (a):
a = (25 m/s) / (2 * t)
To find t, we can substitute the derived value of a and solve for t.
Hmm, I hope I didn't make you miss the bus with all these calculations.
To find the time and acceleration, we can start by organizing the given information:
Initial velocity (Vi) = 0 m/s (bus is starting from rest)
Final velocity (Vf) = 25 m/s
Distance (d) = 1.0 km = 1000 m
To find the time (Δt) and the acceleration (a), we need to use the appropriate kinematic equation. The correct equation to use in this scenario is:
Vf² = Vi² + 2ad
Since the initial velocity (Vi) is 0, the equation simplifies to:
Vf² = 2ad
We can rearrange the equation to solve for the acceleration (a):
a = (Vf²) / (2d)
Now, let's plug in the given values:
a = (25 m/s)² / (2 × 1000 m)
a = 625 m²/s² / 2000 m
a = 0.3125 m/s²
The acceleration of the bus is 0.3125 m/s².
To find the time (Δt), we can use a different kinematic equation:
Δt = (Vf - Vi) / a
In this case, Vi is 0 m/s (starting from rest), so the equation becomes:
Δt = Vf / a
Plugging in the values:
Δt = 25 m/s / 0.3125 m/s²
Δt = 80 s
Therefore, the time taken for the bus to achieve a velocity of 25 m/s is 80 seconds.