question_answer

Diagram shows velocity - time graphs of car P and Q, starting from same place and in same direction. Which car is ahead after 10s and by how much? (a) both cars have the same distance and at the same time (b) car P is ahead by 12.5 m (c) car Q is ahead by 12.5 m (d) none of these

Answer:

  The distance travelled by car ‘P’ = Area of triangle ‘OAB’ \[=\frac{1}{2}\times OB\times AB=\frac{1}{2}\times 10\times 30=175m\] Distance travelled by car Q = Area of trapezium CDEB \[=\frac{1}{2}\times EB\times (DE+CB)=\frac{1}{2}\times 25\times (5+8)\] \[=162.5m\] car ‘P’ is ahead by = (175 - 162.5) m = 12.5 m \[150=10u+\frac{1}{2}a{{(10)}^{2}}\] car P is ahead by 12.5 m.