If an object is traveling at 24 km/h and accelerates at a rate of -.20 m/s2 , how long will it take the object to get to 8 km/h?
To solve this problem, we need to convert the units to be consistent. We can convert the speed from km/h to m/s and then use the equation of motion to find the time it takes for the object to reach the desired speed.
Step 1: Convert the given speed of 24 km/h to m/s.
To convert from km/h to m/s, we can use the conversion factor: 1 km/h = 0.2778 m/s.
So, 24 km/h = 24 * 0.2778 = 6.67 m/s.
Step 2: Convert the desired speed of 8 km/h to m/s.
Following the same method, 8 km/h = 8 * 0.2778 = 2.22 m/s.
Now, we can use the equation of motion to find the time:
v = u + at
where:
v = final velocity
u = initial velocity
a = acceleration
t = time
Rearranging the formula to solve for time (t), we get:
t = (v - u) / a
Plugging in the values:
t = (2.22 m/s - 6.67 m/s) / -0.20 m/s^2
t = -4.45 m/s / -0.20 m/s^2
t = 22.25 s.
Therefore, it will take the object approximately 22.25 seconds to reach a speed of 8 km/h while accelerating at a rate of -0.20 m/s^2.