Question

A car starting from rest has the acceleration 0.5 m/s2. Calculate the velocity and distance travelled by the car after 2 minutes.

Answer 1

Answer :

Distance after 2 minutes = 3600 m

Velocity after 2 minutes = 60 m/s

Explication of steps :

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

• Initial velocity (u) = 0 m/s

[Here, initial velocity is zero because the car is starting from rest.]

• Acceleration (a) = 0.5 m/s²

• Time (t) = 2 minutes

We are asked to calculate the value of final velocity (v) and distance travelled (s) after 2 minutes.

Before commencing the steps, we need to convert minutes into seconds.

★ Converting time taken from minutes into seconds :

$\\ \twoheadrightarrow \sf{\quad { 1 \; minute = 60 \; seconds}}$

$\\ \twoheadrightarrow \sf{\quad { 2 \; minute s= (60 \times 2) \; seconds}}$

$\\ \twoheadrightarrow \sf{\quad { 2 \; minute s= 120 \; seconds}}$

Therefore, time taken is 120 seconds.

★ Calculating the velocity after two minutes (v or final velocity) :

We'll be using the first equation of motion to find the final velocity,

$\\ \twoheadrightarrow \quad \pmb{\boxed{\sf {v = u+at}} }$

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

$\\ \twoheadrightarrow \sf{\quad { v = 0 + ( 0.5 \times 120) }}$

$\\ \twoheadrightarrow \sf{\quad { v = 0 + (60) }}$

$\\ \twoheadrightarrow \sf{\quad { v = 60 \; ms^{-1} }}$

Therefore, velocity of the car after 2 minutes is 60 m/s.

★ Calculating distance travelled :

By using the second equation of motion,

$\\ \twoheadrightarrow \quad \pmb{\boxed{\sf {s = ut + \dfrac{1}{2}at^2 }} }$

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

$\\ \twoheadrightarrow \sf{\quad { s = (0 \times 120) + \dfrac{1}{2} \times 0.5 \times (120)^2}}$

$\\ \twoheadrightarrow \sf{\quad { s = \dfrac{1}{2} \times \dfrac{5}{10} \times 14400}}$

$\\ \twoheadrightarrow \sf{\quad { s = \dfrac{5}{10} \times 7200}}$

$\\ \twoheadrightarrow \sf{\quad { s = 5 \times 720}}$

$\\ \twoheadrightarrow \sf{\quad { s = 3600 \; m}}$

Therefore, distance travelled by the car after 2 minutes is 3600 m.

Answer 2

${\large{\underline{\underline{\pmb{\frak{Let's\ understand\ the\ concept:-}}}}}}$

☀️ As per the given information, we know that the car starts from rest which means it initial velocity was zero and it has the acceleration of 0.5 m/s². In order to find the velocity and distance travelled by car after 2 minutes we can apply the first equation of motion and second equation of motion.

❍  Firstly, we've to convert the given time into seconds and then by solving the equation we have, we can easily find the velocity and distance travelled.

${\large{\underline{\underline{\pmb{\frak{Given:-}}}}}}$

• Initial Velocity ( u ) of car = 0 m/s

• Acceleration ( a ) = 0.5 m/s²

• Time ( t ) = 2 min = 120 seconds

${\large{\underline{\underline{\pmb{\frak{To\;find:-}}}}}}$

• Final velocity ( v )  of car

• Distance travelled ( s ) by car

${\large{\underline{\underline{\pmb{\frak{solution:-}}}}}}$

Finding final velocity :-

★ v = u + at  

[ First equation of motion ]

➟ v = 0 + ( 0.5 × 120 )

➟ v = 0 + 60

➟ v = 60 m/s

Finding distance travelled :-

★ s = ut +  ½ × at²

[ Second equation of motion ]

➟ s = ( 0 × 120 ) +  ½ × ( 0.5 ) × ( 120 )²

➟ s = 0 +  ½ × 0.5 × 14400

➟ s = 0 +  ½ × 7200

➟ s = 0 + 3600

➟ s = 3600 m

___________

Henceforth,

• Velocity and distance travelled by the car after 2 minutes are 60 m/s and 3600 m.