Speed, Distance & Time — Assertion-Reason Type Questions

Assertion (A): A cyclist covers 1.4 km in 240 seconds. His speed is 21 km/hr.

Reason (R): The distance travelled by a moving body in unit time is known as speed.

1. A is true, R is false.

2. A is false, R is true.

3. Both A and R are true.

4. Both A and R are false.

Answer

Given,

A cyclist covers 1.4 km in 240 seconds.

$\text{Time} = 240 \text{ s } = \dfrac{240}{3600} \text{ h } = \dfrac{1}{15} \text{ h }\\[1em] \text{Speed} = \dfrac{\text{Distance}}{\text{Time}} \\[1em] \Rightarrow \text{Speed} = \dfrac{1.4 \text{ km}}{\dfrac{1}{15} \text{ h}}\\[1em] = 1.4 \times 15 \text{ km/h }\\[1em] = 21 \text{ km/h }$

So, Assertion (A) is true.

Speed is defined as the distance travelled by a moving body in unit time. So, Reason (R) is true.

Hence, option 3 is the correct option.

Assertion (A): 7.5 m/s = 27 km/h

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

1. A is true, R is false.

2. A is false, R is true.

3. Both A and R are true.

4. Both A and R are false.

Answer

Solving,

$1 \text{ m } = \dfrac{1}{1000} \text{ km and } 1 \text{ s } = \dfrac{1}{3600} \text{ h }\\[1em] \Rightarrow 7.5 \text{ m/s } = \dfrac{7.5 \times \dfrac{1}{1000} \text{ km}}{\dfrac{1}{3600} \text{ h}}\\[1em] \Rightarrow 7.5 \text{ m/s } = \dfrac{7.5}{1000} \times 3600 \text{ km/h }\\[1em] \Rightarrow 7.5 \text{ m/s } = 27 \text{ km/h }$

So, Assertion (A) is true.

$1 \text{ m/s } = \dfrac{\dfrac{1}{1000} \text{ km}}{\dfrac{1}{3600} \text{ h}}\\[1em] \Rightarrow 1 \text{ m/s } = \dfrac{3600}{1000} \text{ km/h }\\[1em] \Rightarrow 1 \text{ m/s } = \dfrac{18}{5} \text{ km/h }$

So, a speed in m/s is converted into km/h by multiplying it by $\dfrac{18}{5}$. So, Reason (R) is true.

Hence, option 3 is the correct option.

Assertion (A): A man rows 12 km in 1 hr. Distance covered by him in 35 minutes is 7.5 km.

Reason (R): Distance covered = Speed × Time.

1. A is true, R is false.

2. A is false, R is true.

3. Both A and R are true.

4. Both A and R are false.

Answer

Speed = 12 km/h

Time = 35 min = $\dfrac{35}{60} \text{ h } = \dfrac{7}{12} \text{ h }$

Distance = Speed × Time = $12 \times \dfrac{7}{12} \text{ km } = 7 \text{ km }$

and not 7.5 km. So, Assertion (A) is false.

Since $\text{Speed} = \dfrac{\text{Distance}}{\text{Time}}$, we get Distance covered = Speed × Time. So, Reason (R) is true.

Hence, option 2 is the correct option.

Assertion (A): 150 m/min = 2.5 m/sec = 9 km/h

Reason (R): Speed in cm per sec = $\dfrac{\text{Distance in centimeter (cm)}}{\text{Time in seconds (s)}}$

1. A is true, R is false.

2. A is false, R is true.

3. Both A and R are true.

4. Both A and R are false.

Answer

Solving,

1 min = 60 s

$150 \text{ m/min } = \dfrac{150 \text{ m}}{60 \text{ s}} = 2.5 \text{ m/s }\\[1em] 1 \text{ m } = \dfrac{1}{1000} \text{ km and } 1 \text{ s } = \dfrac{1}{3600} \text{ h }\\[1em] \Rightarrow 2.5 \text{ m/s } = \dfrac{2.5 \times \dfrac{1}{1000} \text{ km}}{\dfrac{1}{3600} \text{ h}}\\[1em] \Rightarrow 2.5 \text{ m/s } = \dfrac{2.5}{1000} \times 3600 \text{ km/h }\\[1em] \Rightarrow 2.5 \text{ m/s } = 9 \text{ km/h }$

So, Assertion (A) is true.

Speed in cm per sec = $\dfrac{\text{Distance in centimeter (cm)}}{\text{Time in seconds (s)}}$, when the distance is in cm and the time is in seconds, the speed obtained is in cm per sec. So, Reason (R) is true.

Hence, option 3 is the correct option.