Distance and Speed
Ex 1:

A car is running at 108 km/hr. Express the speed in m/s. Also find the distance covered by the car in 20 seconds ?

Sol:
Given speed = 108 km/hr
= (108 × 1000 )m / (60 × 60 )s
= 30 m/s.
Distance covered by car in 20 seconds = Speed × Time
= 30 m/s × 20 s
= 600 m.
Ex 2:

A car uniformly travels a distance of 72km in 2 hours. Express its speed in kilometres per hour and metres per second ?

Sol:
Given distance d = 72 km and time t = 2 hr.
Then speed = d / t
= 72 km / 2 hr
= 36 km/hr

(OR)

To express the speed in m/s,
speed = d / t
= (72 × 1000)m / (2 × 60 × 60)s
= 10 m/s
Ex 3:

The distance between Amritsar and Delhi is 434 km. It is covered by Shatabdi Express in 6.2 hours. Find the speed of the train in
(i) km/hr
(ii)m/s

Sol:
Distance travelled = 434 km, time taken = 6.2 hrs.
∴ Speed = (Distance traveled) / (Time taken)
= 434 km / 6.2 hrs
= 70 km/hr

To find speed in m/s, we must change the unit of distance to metres and the unit of time to the second.

∴ Speed = (434 ⨯ 1000) m / (6.2 ⨯ 3600) s
= 19.44 m/s.
Ex 4:

A scooterist covers a distance of 5 kilometres in 7 minutes. Calculate his speed in :
(i) centimetres per second (cm/s)
(ii) metres per second (m/s)
(iii) kilometres per hour (km/hr)

Sol:

(i)To calculate the speed in centimetres per second we should convert the given distance of 5 kilometres into centimetres and the given time of 7 minutes into seconds.

Please note that 1 kilometre has 1000 metres and 1 metre has 100 centimetres.
Now, Distance traveled = 5 km
= 5 × 1000 m ---------- (1)
= 5 × 1000 × 100 cm
= 500,000 cm
Time taken = 7 minutes
= 7 × 60 seconds
= 420 s ----------- (2)
We know that, speed = (Distance traveled)/(Time taken)
= 500,000 cm / 420 s
= 1190.48 cm/s -------------- (3)

Thus, the speed of scooterist is 1190.48 centimetres per second.

(ii)To express the speed in metres per second we should convert the given distance of 5 kilometres into metres and the given time of 7 minutes into seconds.

Thus, in this case :
Distance traveled = 5 km
= 5 × 1000 m
= 5000 m -----------(4)
Time taken = 7 minutes
= 7 × 60 seconds
= 420 s --------------(5)
Now, speed = (Distance traveled)/(Time taken)
= 5000 m / 420 s
= 11.90 m/s -------------- (6)

So, the speed of a scooterist is 11.90 metres per second.

(iii) And finally, to calculate the speed in kilometres per hour, we should express the given distance in kilometres (which is already so), and the given time in hours.

So, in this case :
Distance traveled = 5 km ----------- (7)
Time taken = 7 minutes
= 7 / 60 hours------------------- (8)
We know that, speed = (Distance traveled)/(Time taken)
= ((5) km/(7/60)) h
= 42.86 km/h -------------- (9)

Thus, the speed of a scooterist is 42.86 kilometres per hour.