The photo shows the speed-time graph of objects A and B for the first 20 seconds of their journey. Given that both objects start travelling at the same time on the same route, calculate the time taken by object B to overtake object A.
My workings: For overtaking to take place the distance travelled by A must be equal to the distance travelled by B.
Distance travelled by object A after 3 seconds = 3 m
Distance travelled by object B after 3 seconds = $\frac12×3×0.72=$ 1.08 m
Therefore overtaking happens some time after 3 seconds. After this I'm not sure how to find the time taken by B to overtake A.
Best Answer
First of all, calculate how much distance the objects have travelled after 5 seconds, which is when both objects start travelling at constant speed.
B has not overtaken A by 5 seconds, so the overtaking must be at $5+x$ seconds where $x\ge0$. In $5+x$ seconds:
Equating these two expressions gives $x+5=1.2x+3$, which rearranges to $0.2x=2$ or $x=10$. Therefore overtaking occurs at $10+5=15$ seconds.