Question

A car from rest starts and accelerates 6 𝑚/𝑠 2 for 5 𝑠, after which it travels with a constant velocity for 9 𝑠. The brakes are then applied so that it decelerates at 4 𝑚/𝑠 2 . Find the total distance traveled by car.

Answer 1

Given:

$v_1=0\:{\rm m/s},\quad a_1=6\:{\rm m/s^2},\quad t_1=5\:\rm s;$

$a_2=0\:{\rm m/s^2},\quad t_2=9\:\rm s;$

$a_3=-4\:{\rm m/s^2},\quad v_4=0\:\rm m/s.$

The total distance

$$d=d_1+d_2+d_3$$

$$d=(a_1t_1^2/2)+(a_1t_1*t_2)+\left(\frac{v_4^2-(a_1t_1)^2}{2a_3}\right)$$

$$=(6*5^2/2)+(6*5*9)+\left(\frac{0^2-(6*5)^2}{2*(-4)}\right)=457.5\:\rm m$$