Question

A train passes your stop at 17m/s it slow downs near the next stop, to 2/ms it travels 70 m as it slows down how long did it take to slow down

Answer 1

The required time is 7.3[seconds]

Step-by-step explanation:

First, we need to find the deceleration for the slow down, we can do this using the following kinematic equation.

`v^(2)=v_(i)^(2) +2*a*x\\ where:\\v=final velocity [m/s]\\v_(i)=initial velocity [m/s]\\a=acceleration or deceleration [m/s^(2)]\\ x=distance[m]\\2^(2)=17^(2)+2*a*(70)\\  a=-2.03[m/s^2]`

The minus sign means that the train is decreasing its velocity.

Now using another kinematic equation, we cand find the time.

`v=v_(i) + a*t\\v=final velocity [m/s]\\v_(i)=initial velocity [m/s]\\t = time [s]\\a = acceleration [m/s^2]\\`

`2=17+(-2.03)*t\\t=7.3 [s]`