Question

The graph shown illustrates velocity versus time for two cars $A$ and $B$ constrained to move in a straight line. Both cars were at the same position at $t=0\text{s}$. Consider the following statements.
(1) Car $A$ is travelling west and Car $B$ is travelling east.
(2) Car $A$ overtakes Car $B$ at $t=5\text{s}$
(3) Car $A$ overtakes Car $B$ at $t=10\text{s}$.

Which of the following is correct?

• A. Only statement 1 is true
• B. Only statement 2 is true
• C. Only statement 3 is true
• D. Only statements 1 and 2 are true

Answer 1

The correct option is C Only statement 3 is true

Since for both velocities are positive, both are moving in the same direction.
The distance travelled is the magnitude of area under $v–t$ curve.
At $t=10\text{sec}$ area for both is 50 units.
So, car $A$ will overtake car $B$ in $10\text{sec}$.