A car starts at a position of x=6 ft and has a speed of 7 mph. After 24 s the car has a speed of 40 mph. Determine the magnitude of the car's average acceleration during this time.
7 mph = 10.267 ft/s
40 mph = 58.667 ft/s
acceleration = 48.40/24 = 2.017 ft/s^2
That's pretty slow accelerationm.. less that 0.1 g
The initial position does not matter.
To determine the magnitude of the car's average acceleration during this time, we need to use the formula for average acceleration:
Average acceleration (a) = change in velocity (Δv) / change in time (Δt)
First, let's find the change in velocity. The car starts with a speed of 7 mph and after 24 seconds, its speed becomes 40 mph. We can convert these speeds from mph to ft/s for consistency.
7 mph = (7 * 5280) ft / (60 * 60) s = 10.27 ft/s
40 mph = (40 * 5280) ft / (60 * 60) s = 58.67 ft/s
Next, we can calculate the change in velocity:
Δv = final velocity - initial velocity
Δv = 58.67 ft/s - 10.27 ft/s = 48.40 ft/s
Now, let's find the change in time:
Δt = 24 s
Finally, we can calculate the average acceleration:
Average acceleration (a) = Δv / Δt
a = 48.40 ft/s / 24 s
a ≈ 2.02 ft/s²
Therefore, the magnitude of the car's average acceleration during this time is approximately 2.02 ft/s².