Question

A car starts from a rest and reaches a velocity of 50km/h after 2 minutes . Calculate the total distance traveled in meters

Answer 1

Required Answer :

The distance travelled by the car = 833.3 m

Given :

• Initial velocity of the car = 0 m/s
• Final velocity of the car = 50 km/hr
• Time = 2 minutes

To find :

• Distance travelled by the car in metres

Solution :

Firstly, we shall convert the final velocity and time from km/hr and minutes into m/s and seconds respectively.

To convert the final velocity of the car from km/h into m/s, multiply the value by 5/18.

⇒ Final velocity = 50 × 5/18

⇒ Final velocity = 25 × 5/9

⇒ Final velocity = 125/9

⇒ Final velocity = 13.89

Therefore, the final velocity of the car = 125/9 m/s or 13.89 m/s.

To convert the time from minutes into seconds, multiply the value by 60.

[1 minutes = 60 seconds]

⇒ Time = 2 × 60

⇒ Time = 120

Therefore, the time (in seconds) = 120 seconds

Calculating the acceleration of the car by using the first equation of motion :

⇒ First equation of motion :

• v = u + at

where,

• v = Final velocity
• u = Initial velocity
• a = Acceleration
• t = time

Substituting the given values :

⇒ 125/9 = 0 + a × 120

⇒ 125/9 = a × 120

⇒ 125/9 × 1/120 = a

⇒ 125/1080 = a

⇒ 25/216 = a

⇒ 0.11 = a

Acceleration of the car = 0.11 m/s² or 25/216 m/s²

Distance travelled by the car :

⇒ Second equation of motion :

• s = ut + ½ at²

⇒ s = (0)(120) + ½ × 25/216 × (120)²

⇒ s = 0 + ½ × 25/216 × 120 × 120

⇒ s = ½ × 25/216 × 120 × 120

⇒ s = 25/216 × 60 × 120

⇒ s = 25/108 × 30 × 120

⇒ s = 25/54 × 15 × 120

⇒ s = 25/27 × 15 × 60

⇒ s = 25/9 × 5 × 60

⇒ s = 25/3 × 5 × 20

⇒ s = 2500/3

⇒ s = 833.3

Therefore, distance travelled by the car = 833.3 m