Question

A train starts from rest and travels 10 seconds with acceleration a=4-0.3t, then runs for 30 seconds at constant velocity and finally comes to rest by decelerating at 3 m/s^2. Determine the MAGNITUDE of the CONSTANT VELOCITY in m/s.

Answer 1

$v_0=0$ - A train starts from rest

$t=10s$ - the time with acceleration

$a=4-0.3t$

$a_{avr}=\frac{a(t_0=0)+a(t_{10}=10)}{t_{10}-t_0}=\frac{0+1}{10}=0.1$

$v=v_0+\frac{a_{avr}t^2}{2}\\ v=0+\frac{0.1 \cdot 10^2}{2}=5$ m/s

Answer: 5 m/s