Question

6. A bus at rest accelerates uniformly to a velocity of 54 km/h in 20 s. What is the dista
travelled by the bus in 20 s?​

Answer 1

Answer:

150 m

Explanation:

As per the provided information in the given question, we have :

• Initial velocity (u) = 0 m/s [Since, it starts from rest]
• Final velocity (v) = 54 km/h
• Time taken (t) = 20 s

We are asked to calculate the distance travelled by the bus in 20s.

Let us first convert the final velocity into m/s.

★ Converting 54 km/h to m/s :

• In order to convert km/h to m/s, we multiply the value with 5/18.

$\longrightarrow \sf { v = 54 \; km/h}$

$\longrightarrow \sf { v = 54 \times \dfrac{5}{18} \; m/s}$

$\longrightarrow \sf { v = 3 \times 5 \; m/s}$

$\longrightarrow \sf { v = 15 \; m/s}$

Therefore, final velocity (v) is 15 m/s.

Now, as we know that :

$\bigstar \: \boxed{\sf {v^2 - u^2 =2as}}$

• v denotes final velocity
• u denotes initial velocity
• t denotes time
• a denotes acceleration
• s denotes distance travelled

★ Calculating acceleration (a) :

By using the first equation of motion,

$\bigstar \: \boxed{\sf {v = u + at}}$

• v denotes final velocity
• u denotes initial velocity
• t denotes time
• a denotes acceleration

→ 15 = 0 + 20a

→ 15 = 20a

→ $\sf \dfrac{15}{20}$ = a

→ $\pmb{\sf {\dfrac{3}{4} \; m/s^2} }$ = Acceleration

★ Calculating distance travelled (s) :

By using the third equation of motion,

$\bigstar \: \boxed{\sf {v^2 - u^2 =2as}}$

• v = 15 m/s
• u = 0 m/s
• a = $\sf {\dfrac{3}{4} \; m/s^2 }$
• s = ?

→ (15)² - (0)² = 2 × $\sf {\dfrac{3}{4} }$ × s

→ 225 - 0 = $\sf {\dfrac{3}{2} }$ × s

→ 225 = $\sf {\dfrac{3}{2} }$ × s

→ 225 ÷ $\sf {\dfrac{3}{2} }$ = s

→ 225 × $\sf {\dfrac{2}{3} }$ = s

→ 75 × 2 = s

$\longrightarrow \underline{ \boxed{\sf {Distance = 150 \; m }}}\bigstar \:$

Therefore, distance travelled by the bus in 20s is 150 m.

More Information :

Some more formulae :

First equation of motion :

• v = u + at

Second equation of motion :

• s = ut + ½at²

Third equation of motion :

• v² = u² + 2as

Where,

• v denotes final velocity

• u denotes initial velocity

• a denotes acceleration

• s denotes distance

• t denotes time