To find the acceleration of a car that decreases its speed from 20 miles per hour (mph) to 10 mph in a duration of 5 seconds, we can use the formula for acceleration:
Acceleration (a) = (Final Velocity – Initial Velocity) / Time
In this case:
- Initial Velocity (u) = 20 mph
- Final Velocity (v) = 10 mph
- Time (t) = 5 seconds
First, we need to convert miles per hour to feet per second because acceleration is typically measured in feet per second squared (ft/s2). We know that:
1 mph = 1.46667 ft/s
Therefore:
- Initial Velocity in ft/s = 20 mph × 1.46667 = 29.3334 ft/s
- Final Velocity in ft/s = 10 mph × 1.46667 = 14.6667 ft/s
Now we can substitute the velocities into the acceleration formula:
a = (14.6667 ft/s – 29.3334 ft/s) / 5 seconds
a = (-14.6667 ft/s) / 5 seconds = -2.93334 ft/s2
The negative sign indicates that the car is decelerating. Hence, the acceleration of the car is approximately -2.93 ft/s2.