Speed, Time & Distance — Assertion-Reason Questions

Assertion (A): A speed of 72 km/h is equivalent to 20 m/sec.

Reason (R): To convert a speed of km/h in m/sec, we multiply by $\dfrac{5}{18}$.

1. Both Assertion (A) and Reason (R) are true and Reason (R) is the correct explanation of Assertion (A).

2. Both Assertion (A) and Reason (R) are true but Reason (R) is not the correct explanation of Assertion (A).

3. Assertion (A) is true but Reason (R) is false.

4. Assertion (A) is false but Reason (R) is true.

Answer

Converting the speed,

72 km/h = $\left(72 \times \dfrac{5}{18}\right)$ m/sec = 20 m/sec

So, Assertion (A) is true.

$1 \text{ km/h } = \dfrac{1 \times 1000 \text{ m}}{60 \times 60 \text{ sec}}\\[1em] = \dfrac{1000}{3600} \text{ m/sec }\\[1em] = \dfrac{5}{18} \text{ m/sec }$

So, to convert a speed of km/h into m/sec, we multiply by $\dfrac{5}{18}$.

So, Reason (R) is true and is the correct explanation of Assertion (A), since the speed of 72 km/h is converted into 20 m/sec by multiplying it by $\dfrac{5}{18}$.

Hence, option 1 is the correct option.

Assertion (A): A car is running at a speed of 43.2 km/h. It will cover 3.5 km in 5 minutes.

Reason (R): Distance = Speed × Time

1. Both Assertion (A) and Reason (R) are true and Reason (R) is the correct explanation of Assertion (A).

2. Both Assertion (A) and Reason (R) are true but Reason (R) is not the correct explanation of Assertion (A).

3. Assertion (A) is true but Reason (R) is false.

4. Assertion (A) is false but Reason (R) is true.

Answer

Given,

Speed = 43.2 km/h

Time taken = 5 minutes

= $\dfrac{5}{60} \text{ h } = \dfrac{1}{12}$ h

By formula,

$\text{Distance} = \text{Speed} \times \text{Time}\\[1em] = 43.2 \times \dfrac{1}{12} \text{ km }\\[1em] = 3.6 \text{ km }$

The car will cover 3.6 km in 5 minutes and not 3.5 km.

So, Assertion (A) is false.

Since, Speed = $\dfrac{\text{Distance}}{\text{Time}}$, we get Distance = Speed × Time.

So, Reason (R) is true.

Hence, option 4 is the correct option.