A bus starting from rest moves with a uniform acceleration of 0.1 m/s for 2 minutes. Find (i) the speed acquired, (ii) the distance travelled.
Answers
Answer :
➥ The Speed acquired by a bus = 12 m/s
➥ The Distance travelled by a bus = 720 m
Given :
➤ Intial velocity of a bus = 0 m/s
➤ Acceleration of a bus = 0.1 m/s²
➤ Time required by the bus = 2 min
To Find :
➤ Speed required by a bus = ?
➤ Distance travelled by a bus = ?
Required Solution :
According to the given question given that Initial velocity of a bus is 0 m/s because the bus starting from rest, acceleration is 0.1 m/s² and Time taken by a bus is 2 min.
✒ To find the Speed acuired by a bus and Distance travelled by a bus, first we need to convert the time taken by a bus, minute into second, after that we will find the Speed acuiredquired by a bus and Distance travelled by a bus.
◈ Time taken = 2 min
→ Time taken = 2 × 60
→ Time taken = 120 sec
Now, we have Intial velocity, Acceleration, and Time taken by a bus.
- Intial velocity of a bus = 0 m/s
- Acceleration of a bus = 0.1 m/s²
- Time taken by a bus = 120 sec
We can find Final velocity of a bus by using the first equation of motion which says v = u + at.
Here,
- v is the Final velocity in m/s.
- u is the Intial velocity in m/s.
- a is the Acceleration in m/s².
- t is the Time taken in second.
✎ So let's calculate Final velocity (v) !
⇛ v = u + at
⇛ v = 0 + 0.1 × 120
⇛ v = 0 + 12
⇛ v = 12 m/s
║Hence, Speed acquired by a bus is 12 m/s.║
We can find Distance travelled by a bus by using the second equation of motion which says s = ut + ½ at².
Here,
- s is the distance in m.
- u is the Intial velocity in m/s.
- t is the Time taken in second.
- a is the acceleration in m/s².
✎ So let's find Distance travelled (s) !
⇛ s = ut + ½ at²
⇛ s = 0 × 120 + ½ × 0.1 × 120²
⇛ s = 0 + ½ × 0.1 × 120²
⇛ s = 0 + ½ × 0.1 × 14400
⇛ s = 0 + 1 × 0.1 × 7200
⇛ s = 0 + 1 × 720
⇛ s = 0 + 720
⇛ s = 720 m
║Hence, the Distance travelled by bus is 720 m.║
Given :
- Initial Velocity (u) = 0 m/s
- Acceleration (a) = 0.1 m/sec²
- Time (t) = 2 min = 2 × 60 = 120 sec
To Find :
- (a) Speed acquired.
- (b) Distance travelled.
Solution :
- By using first equation motion :]
➥ v = u + at
- Putting all the given values we get :]
➥ v = 0 + 0.1 × 120
➥ v = 0.1 × 120
➥ v = 12 m/s
Therefore, Speed acquired by bus is 12 m/s.
Now, we will find the Distance travelled by bus.
- By using third equation of motion :]
➦ v² - u² = 2as
- Putting all the given values we get :]
➦ (12)² - (0)² = 2 × 0.1 × s
➦ 144 = 0.2s
➦ s = 144/0.2
➦ s = 720 m
Therefore,the Distance travelled by the bus is 720 m.