Question

31.
A car moving with a velocity of 10 ms and with a uniform acceleration gains a velocity of 30 ms
distance of 4 km. The time taken is
-1
after travelling a
A. 20 s​

Answer 1

Appropriate Question :

• A car moving with a velocity of 10 m/s and with a uniform acceleration gains a velocity of 30 m/s after travelling a distance of 4 km. The time taken is ?

Given :

• A car moving with a velocity of 10 m/s and with a uniform acceleration gains a velocity of 30 m/s after travelling a distance of 4 km.

To Find :

• Time taken = ?

Solution :

⛢ Initial Velocity (u) = 10 m/s

⛢ Final Velocity (v) = 30 m/s

⛢ Distance travelled (s) = 4 km

⛢ Acceleration (a) = ?

⛢ Time taken (t) = ?

❒ First of all convert distance travelled by the car from km to m :

→ Distance travelled = 4 km

→ Distance travelled = 4 × 1000

→ Distance travelled = 4000 m

• Hence,the distance travelled by the car is 4000 m.

❒ Now, let's calculate the acceleration of the car by using third equation of motion :

➻ v² = u² + 2as

➻ (30)² = (10)² + 2 × a × 4000

➻ 900 = 100 + 8000a

➻ 900 - 100 = 8000a

➻ 800 = 8000a

➻ a = 800 ÷ 8000

➻ a = 8 ÷ 80

➻ a = 1 ÷ 10

➻ a = 0.1 m/s²

• Hence,the acceleration of the car is 0.1 m/s².

❒ Finding the time taken by the car by using first equation of motion :

➺ v = u + at

➺ 30 = 10 + (0.1)t

➺ 30 - 10 = 0.1t

➺ 20 = 0.1t

➺ t = 20 ÷ 0.1

➺ t = (20 × 10) ÷ (0.1 × 10)

➺ t = 200 ÷ 1

➺ t = 200 seconds

• Hence,the time taken by the car is 200 seconds.

Answer 2

Given:-

• Initial Velocity = 10m/s
• Final Velocity = 30m/s
• Distance = 4km

Find:-

• Time taken by car

Solution:-

→ Distance = 4km

we, will change it into m

→ 1km = 1000m

→ 4km = 4×1000 = 4000m

So, Distance is 4000m.

Now, finding the Acceleration of the car

we, know that

↣v² - u² = 2as «3rd eq. of motion»

where,

• v = 30m/s
• u = 10m/s
• s = 4000m

☯ Substituting these values:

↪v² - u² = 2as

↪(30)² - (10)² = 2a(4000)

↪900 - 100 = 8000a

↪800 = 8000a

↪800/8000 = a

↪1/10 = a

↪a = 0.1m/s²

So, the acceleration of the car is 0.1m/s²

Now, finding the time taken by the car to cover the given distance

we, know that

↬v = u + at ‹1st eq. of motion›

where,

• v = 30m/s
• u = 10m/s
• a = 0.1m/s²

☯ Substituting these values:

⇥v = u + at

⇥30 = 10 + (0.1)t

⇥30 - 10 = 0.1t

⇥20 = 0.1t

⇥20/0.1 = t

⇥200 = t

⇥t = 200sec

Therefore, Time taken by car to cover the given distance is 200sec