Question

5. Calculate the acceleration if an engine starts from rest and moves with uniform
acceleration, attaining a speed of 40 km/h in 10 minutes.​

Answer 1

Given, An engine starts from rest and moves with uniform acceleration, attaining a speed of 40 km/h in 10 minutes.

• To find, Acceleration of engine

Solution :

Initial velocity, u = 0 (as engine starts from rest)

Final velocity, v = 40km/h

Time taken, t = 10 min

• Convert 'km/h' into 'm/s' and 10 min into sec

→ v = 40km/h

→ v = 40 × 5/18

→ v = 11.11 m/s

→ t = 10min. [1 min = 60 seconds]

→ t = 10 × 60

→ t = 600 sec

• According to the first equation of motion

→ v = u + at

→ 11.11 = 0 + a × 600

→ 11.11 = 600a

→ a = 11.11/600

→ a = 0.01851 m/s²

•°• Acceleration of engine is 0.01851 m/s²

Answer 2

Given:-

• An engine starts from rest and moves with uniform acceleration, attaining a speed of 40 km/h in 10 minutes.

To find:-

• Acceleration of an engine

Equation Used:-

• ${\boxed{\bf{First\: Equation\:of\:Motion:v=u+at}}}$

Here,

• v = Final Velocity

• u = Initial Velocity

• a = Acceleration

• t = Time taken

Solution:-

Converting Units:-

$\sf :\implies\:v = 40kmh^{-1}$

$\sf :\implies\:v = 40\times \dfrac{5}{18}\:ms^{-1}$

$\bf :\implies\:v =11.1ms^{-1}$

And,

$\sf :\implies\:t = 10\:min$

$\sf :\implies\:t = 10\times60\:sec$

$\bf :\implies\:t = 600\:sec$

Using first equation of motion,

$\sf :\implies\:v=u+at$

Here,

• v = 11.1 m/s

• u = 0 m/s

• t = 600 sec

Putting values,

$\sf :\implies\:11.1=0+a\times600$

$\sf :\implies\:600a=11.1$

$\sf :\implies\:a=\dfrac{11.1}{600}$

$\sf :\implies\:a=0.0185\:ms^{-2}$

Hence, The acceleration of an engine is 0.0185 m/s².

━━━━━━━━━━━━━━━━━━━━━━━━━