Answer: 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.
