Can You Catch the Bus If It Starts Accelerating While You're Running to It?

[mat331760298]

1. You are running late for your bus that is 100m away. Luckily it is stopped at a traffic light. When you are 16m from the bus, running at your max speed of 6.0m/s the light changes and the bus starts accelerating at 1.0m/s². Do you catch the bus? If so, how far did you have to run to catch it?



2. v1= initial velocity
v2= final velocity
a= acceleration
t= time
d= displacement

1)v2=v1 + at
2)d= 0.5(v2+v1)t
3)d=v1t+0.5at²
4)d=v2t-0.5at²
5)[v2]²=[v1]²+2ad

3. I have answered the question and got that you do catch the bus in 4 seconds time and have to run 24m, but i solved using trial and error. I would like to know how to solve this question using a more algebraic method.

 

[kodadra]

Assuming you caught your bus we can make the two displacements equal each other:
displacement of bus = displacement of you - 16m
d₁ = d₂-16
v₁t+0.5at² = v₂t-16

Then solve for t. There's probably other ways of solving this algebraically, this is just the first one I thought of.