Motions along a straight line

Question

A car moves along an x axis though a distance of 900m, starting at rest (at x=0) and ending at rest (at x =900 m). Through the first \(1/4\) of that distance, its acceleration is +2.25 m/\(s^2\). Through the rest of that distance, its acceleration is -0.750 \(m/s^2\). What are (a) its travel time through the 900m and (b) its maximum speed? (c) Graph position x, velocity v, and acceleration a versus time t for the trip.

Answer 1

(a) The total time of the trip will equal to:

t = t₁+t₂

When t₁ and t₂ are the time of the car traveling with an acceleration equal to a_1/4=2.25 m/s² and a_3/4=-0.750 m/s² respectively. For the first part of traveling:

Now, we can calculate the traveling time using the following equation:

For the second part at which the acceleration value is equal to: a3/4=-0.750 m/s2 we will use the following equation:

Then, the total time of the car traveling will be equal to:

(b)

(c)