At highway speeds, a particular automobile is capable of an acceleration of about 1.6 m/s2. At this rate, how long does it take to accelerate from 81 km/h to 107 km/h?
To find the time it takes to accelerate from 81 km/h to 107 km/h, we need to determine the change in velocity and then use the formula for acceleration:
Acceleration (a) = Change in velocity (Δv) / Time (t)
First, we need to convert the speeds from km/h to m/s:
81 km/h * (1000 m / 1 km) * (1 h / 3600 s) = 22.5 m/s
107 km/h * (1000 m / 1 km) * (1 h / 3600 s) = 29.7 m/s
Now, we can calculate the change in velocity:
Δv = Final velocity - Initial velocity
Δv = 29.7 m/s - 22.5 m/s = 7.2 m/s
Next, we rearrange the formula for acceleration to solve for time:
t = Δv / a
Substituting the values:
t = 7.2 m/s / 1.6 m/s^2 = 4.5 seconds
Therefore, it takes approximately 4.5 seconds to accelerate from 81 km/h to 107 km/h.