a car is stopped at a traffic light, which then turns green. The car speeds up for 85 seconds and travels a distance of 1.5 miles. what is the car's acceleration from the traffic light?
Well, it seems like this car really wanted to make a green statement! To calculate acceleration, we need to know the change in velocity and the time it took. Since the car was initially at rest, its change in velocity is the final velocity, which is the speed it reached after 85 seconds.
But, hold your horses! We're missing some information here. We don't know the final speed of the car after 85 seconds. So, unless we have that information, we can't calculate the car's acceleration. Let's hope the car stops for a coffee break and gives us more details!
To find the car's acceleration from the traffic light, we can use the formula:
Acceleration (a) = (Final velocity (v) - Initial velocity (u)) / Time taken (t)
Given:
Initial velocity (u) = 0 mph (since the car was stopped)
Final velocity (v) = distance / time = 1.5 miles / 85 seconds
Let's calculate the acceleration:
Acceleration (a) = (1.5 miles / 85 seconds - 0 mph) / 85 seconds
Acceleration (a) = 1.5 miles / (85 seconds * 85 seconds)
Acceleration (a) = 1.5 miles / 7225 seconds^2
The car's acceleration from the traffic light is approximately 0.0002 miles/second^2.
To find the car's acceleration, we need to use the formula:
acceleration (a) = change in velocity (Δv) / time interval (Δt)
In this case, we have the time interval (Δt) of 85 seconds and need to find the change in velocity (Δv) to calculate the acceleration.
Since the car starts from rest at the traffic light, we can assume its initial velocity (v₀) is 0 mph. The final velocity (v) can be calculated using the equation:
distance (d) = average velocity (v̅) × time (t)
In this case, the car's average velocity can be calculated as:
average velocity (v̅) = distance (d) / time (t) = 1.5 miles / 85 seconds
Now, to find the final velocity (v), we multiply the average velocity (v̅) by 2 since the car's speed is continuously increasing over the 85-second interval.
final velocity (v) = 2 × average velocity (v̅)
Finally, we can calculate the change in velocity (Δv) by subtracting the initial velocity (v₀) from the final velocity (v).
change in velocity (Δv) = final velocity (v) - initial velocity (v₀)
With the value of Δv and Δt, we can now calculate the car's acceleration (a) using the formula mentioned earlier:
acceleration (a) = change in velocity (Δv) / time interval (Δt)
By following these steps, you should be able to calculate the car's acceleration from the traffic light.