An initially motionless test car is accelerated uniformly to 135 km/h in 8.08 seconds before striking a simulated deer. The car is in contact with the faux fawn for 0.695 seconds, after which the car is measured to be traveling at 87.5 km/h. What is the magnitude of the average acceleration of the car during the collision?
Well, this faux fawn seems to have caused quite the commotion! To find the magnitude of average acceleration during the collision, we first need to figure out the change in velocity.
From 135 km/h to 87.5 km/h, it's like the car said, "Wait, deer not!" and slowed down.
So, using the formula (final velocity - initial velocity) / time, we have:
(87.5 km/h - 135 km/h) / 0.695 s
This gives us a change in velocity of -47.5 km/h over 0.695 seconds.
Now, to be proper scientists, we need to convert those pesky kilometers per hour into meters per second. You never know when a deer might be hiding behind a meter stick!
So, let's multiply by a conversion factor of 1000 m/3600 s. That's because there are 1000 meters in a kilometer and 3600 seconds in an hour.
After all the multiplication and division, we're left with a change in velocity of -13.2 m/s over 0.695 seconds.
That's a negative change because the car was slowing down.
Finally, we divide the change in velocity by the time to get the average acceleration:
-13.2 m/s / 0.695 s ≈ -19 m/s^2
So, the magnitude of the average acceleration during the collision is approximately 19 meters per second squared. It looks like the car hit the brakes faster than a deer in headlights!
To find the magnitude of the average acceleration of the car during the collision, we need to calculate the change in velocity and the time interval during the collision.
First, let's convert the initial and final velocities from km/h to m/s since acceleration is typically measured in meters per second squared (m/s^2).
Initial velocity (u) = 0 km/h (since the car is initially motionless)
Final velocity (v) = 87.5 km/h
1 km/h is equal to 0.2778 m/s, so we can convert the velocities as follows:
Initial velocity (u) = 0 km/h = 0 m/s
Final velocity (v) = 87.5 km/h * 0.2778 m/s/km/h = 24.3056 m/s
Now, let's calculate the change in velocity (Δv) during the collision:
Δv = Final velocity (v) - Initial velocity (u)
Δv = 24.3056 m/s - 0 m/s
Δv = 24.3056 m/s
Next, let's calculate the time interval (Δt) during the collision. We are given that the car is in contact with the faux fawn for 0.695 seconds.
Δt = 0.695 seconds
Finally, we can calculate the average acceleration (a) using the formula:
a = Δv / Δt
Substituting the values we found, we get:
a = 24.3056 m/s / 0.695 seconds
Calculating this expression, the average acceleration of the car during the collision is approximately:
a = 34.9667 m/s^2
So, the magnitude of the average acceleration of the car during the collision is approximately 34.97 m/s^2.