Originally Posted by **sensei** The speed of a train increases at a constant rate α = 1 m/s^2 from 0 to v = 10 m/s and then remains constant for a time interval and finally decreases to zero at a constant rate β = 2m/s^2. If l = 100 m is the total distance covered then total time taken is?
A) 17.5 s
B) 2.0 s
C) 13.2 s
D) None of these |

My advice:

Break the problem into three time frames.

For the first acceleration period you know that

$\displaystyle v = at_1$

so you can find $\displaystyle t_1$. We will also need to know $\displaystyle x_1$, so

$\displaystyle v^2 = 2ax_1$.

For the constant speed period you know that:

$\displaystyle x_2 = vt_2$

We don't yet know x_2, so we are stuck on this for a moment.

For the second accleration (deceleration) period we have

$\displaystyle v = -at_3$

(The acceleration is negative here, so the negative signs cancel.) So we can find $\displaystyle t_3$.

Again,

$\displaystyle v^2 = -2ax_3$

so we can find $\displaystyle x_3$ from this.

Now, $\displaystyle x_2 = 100 - x_1 - x_3$ so you can now find $\displaystyle x_2$ and thus $\displaystyle t_2$. Now just add your times.

-Dan