A motorist enters a freeway at 25 mi/h and accelerates uniformly to 65 mi/h. From the odometer in the car, the motorist knows that she traveled 0.1 mi while accelerating. Determine (a) the acceleration of the car, (b) the time required to reach 65 mi/h.

a) 2.2 m/s² b) 8 s

Explanation:

a) Assuming that the acceleration is constant, we can use any of the kinematic equations to solve the question.

As we don't know the time needed to accelerate, we can use the following equation:

vf2 - vo2 = 2*a*∆x

At first, we can convert the values of vf, vo and ∆x, to SI units, as follows:

vf = 65 mi/h * (1,605 m / 1mi) * (1h/3,600 sec) = 29 m/s

vo = 25 mi/h * (1,605 m / 1mi) * (1h/3,600 sec) = 11.2 m/s

∆x = 0.1 mi * (1,605 m / 1mi) = 160.5 m

Replacing these values in (1), and solving for a, we have:

a = (29 m/s - 11.2 m/s) / 321 m = 2.2 m/s2

b) In order to obtain the time needed to reach to 65 mi/h, we can rearrange the equation for the definition of acceleration, as follows:

vf = vo + at

Replacing by the values already known for vo, vf and a, and solving for t, we get:

t = vf-vo / a = (29 m/s - 11.2 m/s) / 2.2 m/s = 8 sec