A car travelling at a constant velocity of $20m/s$ passes a stationary sport car. Ten seconds afterwards the sport car accelerates uniformly at $3m/s²$ to reach a speed of $30m/s$ with which it continues. Find when and where the sport car overtakes the first car.
How to indicate the bolded on a velocity time graph is the problem I'm having and hence finding a solution to the problem.
Hint. First of all recall the main equations of one-dimensional kinematics.
Let $v_c(t)$ and $v_s(t)$ be the velocity at time $t$ of the car and the sport car respectively. At time $t=0$, the travelling car passes the stationary sport car at the origin. Then for $t\geq 0$, $$v_c(t)=20\quad\text{and}\quad v_s(t)=\begin{cases} 0&\text{for $t\leq 10$,}\\ 3(t-10)&\text{for $10<t\leq t_1$,}\\ 30&\text{for $t_1<t$.} \end{cases}$$ where $t_1$ is a time to be found. Can you take it from here?