A certain car is capable of accelerating at a rate of 0.56 m/s2. How long does it take for this car to go from a speed of 25 mi/h to a speed of 32 mi/h?
To find the time it takes for the car to go from a speed of 25 mi/h to 32 mi/h, we need to use the acceleration and the initial and final speeds.
First, we need to convert the speeds from miles per hour (mi/h) to meters per second (m/s) since the acceleration is given in m/s².
To convert miles per hour to meters per second, we can use the following conversion factors:
1 mile = 1609.34 meters
1 hour = 3600 seconds
For the initial speed of 25 mi/h:
25 mi/h * (1609.34 meters/1 mile) * (1 hour/3600 seconds) = 11.176 m/s
For the final speed of 32 mi/h:
32 mi/h * (1609.34 meters/1 mile) * (1 hour/3600 seconds) = 14.331 m/s
Now that we have the initial speed (11.176 m/s), final speed (14.331 m/s), and acceleration (0.56 m/s²), we can use the formula for calculating time:
final speed = initial speed + (acceleration * time)
Rearranging the formula to solve for time:
time = (final speed - initial speed) / acceleration
Substituting the values:
time = (14.331 m/s - 11.176 m/s) / 0.56 m/s²
Simplifying:
time = 3.155 m/s / 0.56 m/s²
time ≈ 5.63 seconds
Therefore, it takes approximately 5.63 seconds for the car to go from a speed of 25 mi/h to a speed of 32 mi/h.