Question

What is the final speed of a car that accelerates at 40 ft/s2 for 1 seconds if it's initial speed was 13 miles per hour, to 1 decimal place?

___ miles/hour.

Answer 1

To find the car's final speed in miles per hour after accelerating for 1 second, convert the initial speed to feet per second, calculate using the acceleration, then convert back to miles per hour. The final speed is approximately 40.2 miles per hour.

Step-by-step explanation:

To calculate the final speed of a car that accelerates at 40 ft/s2 for 1 second with an initial speed of 13 miles per hour, we must first convert the speeds to the same unit of measurement. Since acceleration is given in feet per second squared, converting the initial speed to feet per second is appropriate. One mile per hour is equivalent to 1.467 feet per second, so:

Initial speed = 13 mi/h = 13 × 1.467 ft/s ≈ 19.071 ft/s

Final speed = initial speed + (acceleration × time)

Final speed = 19.071 ft/s + (40 ft/s2 × 1 s) = 59.071 ft/s

Now, we convert the final speed back to miles per hour:

Final speed = 59.071 ft/s ÷ 1.467 ft/s per mi/h ≈ 40.2 mi/h