Question

you are standing at rest on the road and another bicyclist passes you moving at a constant speed of 10m/s . At the moment the other cyclist is 75m ahead of you on the road , you begin riding in the same direction with a constant acceleration of 2m/s^2 . how long will it take for you catch up to the other cyclist?

Answer 1

equation of motion for another bicycle: 75+10t
\[x=x_0+vt=75+10t\]
equation of motion for you
\[x=at^2/2=t^2\]
to catch you need to be at same position at same time:
75+10t=t^2
you need to solve this equation for t