A model engine accelerates

Question

A model engine accelerates forward from rest along a straight track at 10.0 m/s^2 for 3.0 seconds. It then accelerates forward at 16 m/s^2 for 5.0 seconds, and finally decelerates at 12 m/s^2 until it stops.

(a) Calculate how many seconds the engine was moving. Answer:

(b) What was its maximum velocity? Answer

(c) Find the total distance travelled. Answer

Answer 1

Hi Matthew!

This is a kinematics problem, and so throughout my explanation I'll be using the following kinematics equations:

1. v = v₀ + at
2. x = (v₀+v)t/2
3. x = x₀ + v₀t + .5at²

a) We are being asked to find the total time traveled. We know that the train travels for 8 seconds, and then begins decelerating at 12 m/s^2. If we find the velocity the train has at t = 8 s, v_f, we can use equation (1) to calculate the time it takes to then reach a speed of 0 m/s. How do we find v_f? Use equation (1) again, since we are given the accelerations from t= 0 to t= 3 and from t=3 to t = 8.

b) In doing part a, you should have found the maximal velocity, which occurs right before the train begins decelerating.

c) You can use either equation 2 or equation 3 to answer this - make sure to apply the equation separately to each time region with different acceleration!