At highway speeds a car can accelerate at 1.7 m/s2. At this rate how long does it take to accelerate from
23.6 m/s to 27.8 m/s?

2.5 seconds

Explanation:

We know that the acceleration is:

a(t) = 1.7 m/s^2

To get the velocity function, we must integrate over time, and we will get:

v(t) = (1.7m/s^2)*t + v0

Where v0 is the initial velocity, in this case, we assume that we start at 23.6m/s, then the initial velocity is:

v0 = 23.6 m/s

Then the velocity equation is:

v(t) =  (1.7m/s^2)*t + 23.6 m/s

Now we want to find the value of t such v(t) = 27.8 m/s

Then:

v(t) =  27.8 m/s =  (1.7m/s^2)*t + 23.6 m/s

        27.8 m/s  - 23.6 m/s =  (1.7m/s^2)*t

         4.2 m/s = (1.7m/s^2)*t

         4.2m/s/(1.7m/s^2) = t = 2.5 s

Then at that acceleration, you need 2.5 seconds.

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