Question

Starting from a stationary position a bus attains a velocity of 6m/s in 30s .Then the driver of the bus applies a brake such that the velocity of the bus comes down to 4m/s in the next 5s .Calculate the arceleration of the bus in both cases.​

Answer 1

QUESTION ⤵️

Starting from a stationary position a bus attains a velocity of 6m/s in 30s .Then the driver of the bus applies a brake such that the velocity of the bus comes down to 4m/s in the next 5s .Calculate the arceleration of the bus in both cases.

ANSWER ⤵️

GIVEN:-

For the case 1 ( from stationary to 6m/s in 30sec)

Initial velocity (u) = 0m/s ( stationary)

Final velocity (v) = 6m/s

Time (t) = 30sec

Acceleration = v-u/t

====> 6 -0/30

====> 6/30

====> 1/5 m/sec² or 0.2 m/sec²

For the case 2 ( from 6m/s to 4m/s in 5sec)

Initial velocity (u) = 6m/s

Final velocity (v) = 4m/s

Time (t) = 5 sec

Acceleration = v-u/t

====> 4-6/5

====> -2/5

====> -2/5 m/sec² or -0.4 m/sec²

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Answer 2

Case ❶ :

Answer :

›»› The acceleration of bus is 0.2 m/s².

Explanation :

Given :

• Initial velocity of bus = 0 m/s.
• Final velocity of bus = 6 m/s.
• Time taken by bus = 30 sec.

To Find :

• Acceleration of bus = ?

Formula required :

Formula to calculate the acceleration of bus is given by,

→ v = u + at.

Here,

• v is the Final velocity of bus.
• u is the Initial velocity of bus.
• a is the Acceleration of bus.
• t is the Time taken by bus.

Units,

• The unit of Final velocity is m/s.
• The unit of Initial velocity is m/s.
• The unit of Acceleration is m/s².
• The unit of Time taken is second.

This formula is known as first equation of motion.

Solution :

As we are given with the initial velocity of bus, final velocity of bus and time taken by bus then we have the required formula of second equation of motion to calculate the acceleration of bus that is,

→ v = u + at.

By using the formula of second equation of motion to calculate the acceleration of bus and substituting all the given values in the formula, we get :

→ 6 = 0 + a × 30

→ 6 = 0 + 30a

→ 6 = 30a

→ a = 6/30

→ a = 0.2.

Hence, the acceleration of bus is 0.2 m/s².

Case ❷ :

Answer :

›»› The acceleration of bus is 0.4 m/s².

Explanation :

Given :

• Initial velocity of bus = 6 m/s.
• Final velocity of bus = 4 m/s.
• Time taken by car = 5 sec.

To Find :

• Acceleration of bus = ?

Formula required :

Formula to calculate the acceleration of bus is given by,

→ v = u + at.

Here,

• v is the Final velocity of bus.
• u is the Initial velocity of bus.
• a is the Acceleration of bus.
• t is the Time taken by bus.

Units,

• The unit of Final velocity is m/s.
• The unit of Initial velocity is m/s.
• The unit of Acceleration is m/s².
• The unit of Time taken is second.

This formula is known as first equation of motion.

Solution :

As we are given with the initial velocity of bus, final velocity of bus and time taken by bus then we have the required formula of second equation of motion to calculate the acceleration of bus that is,

→ v = u + at.

By using the formula of second equation of motion to calculate the acceleration of bus and substituting all the given values in the formula, we get :

→ 4 = 6 + a × 5

→ 4 = 6 + 5a

→ 4 - 6 = 5a

→ -2 = 5a

→ a = -2/5

→ a = -0.4.

Here negative sign indicate retardation.

Hence, the acceleration of bus is 0.4 m/s².