Idea of Speed, Distance & Time — Assertion Reason Type Questions

Assertion (A) : A cyclist covers 200 m in 40 sec, his speed is 18 km/h.

Reason (R) : Speed in km/h = (speed in m/s) × $\dfrac{18}{5}$

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

For the cyclist :

Speed = $\dfrac{\text{Distance}}{\text{Time}} = \dfrac{200}{40} = 5$ m/s.

Converting into km/h (multiply by $\dfrac{18}{5}$) :

Speed = 5 × $\dfrac{18}{5} = 18$ km/h.

So, Assertion (A) is true.

To convert a speed from m/s to km/h, we multiply by $\dfrac{18}{5}$, i.e. speed in km/h = (speed in m/s) × $\dfrac{18}{5}$, which is correct.

So, Reason (R) is true.

Hence, option 3 is the correct option.

Assertion (A) : A car moving with a speed of 60 km/h covers a certain distance in 3 hrs. The time taken by the car to cover the same distance with the speed of 50 km/h is $\dfrac{60 \times 3}{50}$ hrs.

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

Distance covered by the car = Speed × time = 60 × 3 = 180 km.

Time taken to cover the same distance at 50 km/h

= $\dfrac{\text{Distance}}{\text{Speed}} = \dfrac{180}{50} = \dfrac{60 \times 3}{50}$ hrs.

So, Assertion (A) is true.

The distance was found using Distance covered = Speed × time (60 × 3 = 180 km).

So, Reason (R) is true.

Hence, option 3 is the correct option.