2019 A/L Physics Past Paper · Question 40 (English Medium)

A lamp post and two cars — displacement–time graphs

The figure shows the displacement-time graphs for the motion of two cars with respect to a lamp post aside the road. Consider the displacement to the right side of the lamp post as positive. A student has made the following statements regarding the motion of cars relevant to the points $P$ , $Q$ , and $R$ marked on the graph.

(A) Relevant to $P$ : Car 1 coming from left crosses Car 2.

(B) Relevant to $Q$ : Both cars are moving towards the lamp post and cross each other.

Which of the above statements is/are correct?

(1) Only B
(2) Only C
(3) Only A and B
(4) Only B and C
(5) All A, B, and C

Answer and explanation

Answer: (2) Only C

What the question asks

We want: which of the statements A, B and C are correct.

$P$ is where the graph of car 1 crosses the time axis.

$Q$ is where the two graphs cross.

$R$ is where the graph of car 2 crosses the time axis.

Relevant theory

gradient = velocity of the body

How to read the graph:

The height of a point is the car's displacement from the post. Right is +.

The gradient is the velocity.

When a graph crosses the time axis, that car is at the post.

When two graphs cross, both cars are at the same place at the same time. They pass each other.

Car 1's gradient is +. It moves to the right.

Car 2's gradient is −. It moves to the left.

Reading the options

The options are: only B, only C, A and B, B and C, all three.

We test each statement. Then we compare.

Reasoning and calculation

$P$ : car 1 passes car 2

At $P$ , car 1 is at the post.

At that moment car 2 is right of the post.

The two cars are not at the same place. So A is wrong.

$Q$ : both cars, moving towards the post, pass each other

At $Q$ the two cars pass each other, right of the post.

Car 1 moves to the right. So it moves away from the post.

Only car 2 moves towards the post. So B is wrong.

$R$ : car 2, coming from the right, passes the post

At $R$ the graph of car 2 crosses the time axis. So car 2 is at the post.

Its gradient is −. So it moves from right to left.

So car 2, coming from the right, passes the post. C is correct.

A and B make the same kind of mistake.

They mix up a graph crossing the time axis with two graphs crossing.

Or they do not read the direction from the sign of the gradient.

Why the other options fail

This option says: only B is correct.

But B is wrong. At $Q$ car 1 moves away from the post. Also, C is correct, and this option leaves it out.

So it is wrong.

This option says: only A and B are correct.

But A is wrong. At $P$ car 1 passes the post, not car 2. B is wrong too.

This option says: only B and C are correct.

C is correct. But B is wrong, because at $Q$ car 1 moves away from the post.

This option says: A, B and C are all correct.

But A and B are wrong. At $P$ car 1 passes the post. At $Q$ car 1 moves away from the post.

Conclusion

$P$ : car 1 passes the post. So A is wrong.

$Q$ : the cars meet, but car 1 moves away from the post. So B is wrong.

$R$ : car 2 passes the post. So C is correct.

So the answer is option (2): only C.

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