Question

A bus starting from rest moves
with a uniform acceleration of
0.1 m s-2 for 2 minutes. Find (a)
the speed acquired; (b) the
distance travelled.​

Answer 1

$\large{\underline{\textsf{\textbf{ Answer : }}}}$

• Speed acquired (v) = 12 m/s
• Distance travelled (s) = 720 m

$\large{\underline{\textsf{\textbf{ Explication \; of \; steps : }}}}$

Given Information :

• Initial velocity (u) = 0 [As it was at rest]

• Acceleration (a) = 0.1 m/s²

• Time = 2 minutes ⇒ 120 seconds

• 1 minute = 60 seconds, so 2 minutes = (2 × 60) ⇒ 120 seconds

To calculate :

• Speed acquired i.e, final velocity (v).

• Distance travelled (s)

Calculations

$\underline{ \bf {\maltese \; \; \; Finding \: speed \: acquired \: (v) : \; \; \; }}$

By using the first question of motion,

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

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

$\longrightarrow \sf { v = 0 + ( 0.1 \times 120) }$

$\longrightarrow \sf { v = 0 + \Bigg ( \dfrac{1}{\cancel{10}} \times \cancel{120} \Bigg ) }$

$\longrightarrow \sf { v = 0 + ( 1 \times 12) }$

$\longrightarrow \sf { v = 0 + 12 }$

$\longrightarrow \sf \red { v = 12 \: m/s }$

Therefore, the speed acquired is 12 m/s.

$\underline{\small \bf {\maltese \; \; \; Finding \: distance\: (s) : \; \; \; }}$

By using the second equation of motion,

$\bigstar \: \boxed{\sf {s = ut + \dfrac{1}{2}at^2}}$

• s denotes distance
• u denotes initial velocity
• a denotes acceleration
• t denotes time

$\longrightarrow \sf {s = ( 0\times 120) + \dfrac{1}{2} \times 0.1 \times (120)^2 }$

$\longrightarrow \sf {s = \dfrac{1}{2} \times 0.1 \times 14400 }$

$\longrightarrow \sf {s = \dfrac{1}{2} \times \dfrac{1}{10} \times 14400 }$

$\longrightarrow \sf {s = \dfrac{1}{2} \times 1440 }$

$\longrightarrow \sf \red{s = 720 \: m }$

Therefore, distance travelled is 720 m.

⠀⠀⠀_____________________

Three equations of motion :

• v = u + at
• s = ut + $\sf \dfrac{1}{2} at^2$
• $\sf v^2 - u^2 = 2as$

• v denotes final velocity.

• s denotes distance

• u denotes initial velocity

• a denotes acceleration

• t denotes time

Answer 2

Explanation:

a) V= U+AT

0.1×120

12 m/sec

Speed acquired= 12m/sec

b) D= S= UT+AT²/2

D = 0.1× 120²/2

D= 14400/10×1/2

D= 720 m

The distance travelled= 720 m

1. 12m/ sec
2. 720m = 0.72 km