Question

A car starts from 0 m along a road and accelerates at 0.5 m/s^2 to the right. A second car starts from 1000 m along the road and accelerates at 1.5 m/s^2 to the left. Both cars started from rest. How long after the start do the cars meet? a) 18.3 s b) 21.2 s c) 22.4 s d) 28.6 s e) 31.6 s

Answer 1

e) 31.6 seconds

Step-by-step explanation:

t = Time taken

u = Initial velocity

v = Final velocity

s = Displacement

a = Acceleration

Equation of motion

`s=ut+(1)/(2)at^2\\\Rightarrow s_1=0* t+(1)/(2)* 0.5* t^2\\\Rightarrow s_1=(1)/(2)0.5t^2\ m`

`s=ut+(1)/(2)at^2\\\Rightarrow s_2=0* t+(1)/(2)* 0.5* t^2\\\Rightarrow s_2=(1)/(2)1.5t^2\ m`

`s_1+s_2=1000`

`\\\Rightarrow 1000=(1)/(2)0.5t^2+(1)/(2)1.5t^2\\\Rightarrow 1000=(0.5t^2+1.5t^2)/(2)\\\Rightarrow 1000=(2t^2)/(2)\\\Rightarrow 1000=t^2\\\Rightarrow t=√(1000)\\\Rightarrow t=31.6\ s`

Time taken by the cars to meet 31.6 seconds.