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 79 km/h to 102 km/h?
To find how long it takes to accelerate from 79 km/h to 102 km/h, we first need to convert the given speeds into meters per second (m/s). The conversion factor is 1 km/h = 0.278 m/s.
First, we convert 79 km/h to m/s:
79 km/h * 0.278 m/s = 21.962 m/s (rounded to three decimal places)
Next, we convert 102 km/h to m/s:
102 km/h * 0.278 m/s = 28.356 m/s (rounded to three decimal places)
Now we have the initial velocity (21.962 m/s) and the final velocity (28.356 m/s) of the car. We can use the formula for time, acceleration, initial velocity, and final velocity:
final velocity = initial velocity + (acceleration * time)
We can rearrange the equation to solve for time:
time = (final velocity - initial velocity) / acceleration
Plugging in the values we have:
time = (28.356 m/s - 21.962 m/s) / 1.6 m/s^2
time = 6.394 m/s / 1.6 m/s^2
time ≈ 3.996 seconds (rounded to three decimal places)
Therefore, it takes approximately 3.996 seconds to accelerate from 79 km/h to 102 km/h.