Question

When a train is traveling along a straight track at 3 m/s, it begins to accelerate at a = (40 V-4) m/s2, where V is in m/s. Determine its velocity, V in m/s after 4 seconds

Answer 1

Solution:

We know that acceleration is

a = dv/dt

We will isolate for dt

dt = dv/a

To find the velocity after 4 seconds we will integrate the left from 0 to 4 seconds. On the right side, we now the initial velocity to be 3m/s and we will integrate from 3 to v where v is final velocity

4 = 1/200 (v^5 - 243)

Solve for v, we get

800 = v^5 - 243

v = 4.01 m/s

Now, we will use the kinematic equation

a ds =v dv

Isolate for ds

ds= vdv/a

Remember that

ds = vdv/a = 1/40 v^5dv

Integrating both sides, we get

s = 1/40

s = 14.41 m