Question

A car travels at 54 km/h for first 20 s, 36 km/h for next 30 s and finally 18 km/h for next 10 s. Find its average speed.

Answer 1

GIVEn

A car travels at 54 km/h for first 20 s, 36 km/h for next 30 s and finally 18 km/h for next 10 s.

TO FINd

Find the average speed

SOLUTIOn

A car travels at 54 km/h for first 20 s, 36 km/h for next 30 s and finally 18 km/h for next 10 s

★ In first case ★

• Speed = 54km/h
• time taken (t1) = 20sec
• Distance = ?

➡ speed = 54 km/h

➡ speed = 54 × 5/18

➡ speed = 15 m/s

*Let the distance be D1*

➡ Distance = time × speed

➡ D1 = 20 × 15

➡ D1 = 300 m

__________________________

★ In second case ★

• Speed = 36 km/h
• time taken (t2) = 30 sec
• Distance = ?

➡ Speed = 36 km/h

➡ speed = 36 × 5/18

➡ speed = 10 m/s

*Let the distance be D2*

➡ Distance = time × speed

➡ D2 = 30 × 10

➡ D2 = 300 m

__________________________

★ In third case ★

• speed = 18km/h
• time taken (t3) = 10sec
• Distance = ?

➡ speed = 18km/h

➡ speed = 18 × 5/18

➡ speed = 5m/s

*Let the distance be D3*

➡ Distance = time × speed

➡ D3 = 10 × 5

➡ D3 = 50 m

Now,

$\implies\sf Average\:speed= \dfrac{Total\: distance\: travelled}{total\:time\:taken} \\ \\ \\ \implies\sf \dfrac{D1+D2+D3}{t1+t2+t3} \\ \\ \\ \implies\sf \dfrac{300+300+50}{20+30+10} \\ \\ \\ \implies\sf \cancel\dfrac{650}{60} \\ \\ \\ \implies\sf 10.8m/s$

Answer 2

GIVEN :-

A car travels at 54 km/h for first 20 s, 36 km/h for next 30 s and finally 18 km/h for next 10 s.

TO FIND :-

The average speed of the car.

FORMULAS TO BE USED :-

• x km/h = x × (5/18) m/s

• Distance = Speed × Time

• Average speed = Total distance covered/Total time taken

SOLUTION :-

For first 20 s,

Speed = 54 km/h = 15 m/s

Time = 20 s

Distance = Speed × time

⇒Distance = 15 × 20

⇒Distance = 300 m

$\rule{150}{2}$

For next 30 s,

Speed = 36 km/h = 10 m/s

Time = 30 s

Distance = Speed × time

⇒Distance = 10 × 30

⇒Distance = 300 m

$\rule{150}{2}$

For next 10 s,

Speed = 18 km/h = 5 m/s

Time = 10 s

Distance = Speed × time

⇒Distance = 5 × 10

⇒Distance = 50 m

$\rule{150}{2}$

Total distance covered = 300 + 300 + 50 = 650 m

Total time taken = 20 + 30 + 10 = 60 s

Average speed = 650/60

⇒Average speed = 65/6

Average speed = 10.8 m/s