Question

A car
moves with uniform
velocity of 40 ms for 5 s. It
comes to rest in the next 10 s s
with uniform deceleration. Find
(i) deceleration (ii) total
distance travelled by the car.
(using equations of motion)​

Answer 1

Given :

• A car moves with uniform velocity of 40 m/s for 5 s.
• It comes to rest in the next 10 s with uniform deceleration.

To find :

• Decelaration of the car
• Total distance travelled by the car

Knowledge Required :

First equation of motion :-

• v = u + at

Third equation of motion :-

• v² - u² = 2as

where,

• v = Final velocity
• u = Initial velocity
• a = Acceleration
• t = Time
• s = Distance

Formula of distance :-

• Distance = Speed × Time

Solution :

• Deceleration :-

Using first equation of motion,

→ v = u + at

We have,

• v = 0 m/s
• u = 40 m/s
• t = 10 s

⇒ 0 = 40 + a × 10

⇒ - 40 = 10a

⇒ - 40 ÷ 10 = a

⇒ - 4 = a

Acceleration of the car = - 4 m/s²

Negative acceleration is known as decelaration.

★ Therefore, deceleration of the car = 4 m/s²

• Total distance travelled :-

Distance travelled in the first five seconds :-

Using formula,

→ Distance = Speed × Time

we have,

• Speed = 40 m/s
• Time = 5 s

⇒ Distance = 40 × 5

⇒ Distance = 200

Distance travelled in first five seconds = 200 m

Distance travelled in next ten seconds :-

Using third equation of motion,

→ v² - u² = 2as

we have,

• v = 0 m/s
• u = 40 m/s
• a = - 4 m/s²
• s = ?

⇒ 0² - 40² = 2 × (- 4) × s

⇒ - 1600 = - 8s

⇒ - 1600 ÷ - 8 = s

⇒ 200 = s

Distance travelled in next ten seconds = 200 m

Total distance travelled = Distance travelled in first 5 seconds + Distance travelled in next ten seconds

= 200 + 200 = 400 m

★ Total distance travelled by the car = 400 m

Answer 2

Answer:

Given :-

• A car moves uniform velocity of 40 m/s for 5 secs. It comes to rest in the next 10 secs with uniform deceleration.

To Find :-

1. What is the deceleration
2. What is the distance travelled by the car.

Formula Used :-

➲ v = u + at

➲ s = ut + ½at²

where,

• v = Final Velocity
• u = Initial Velocity
• a = Acceleration
• t = Time
• s = Distance travelled

Solution :-

(i) To find declaration,

Given :

• Final velocity = 0 m/s
• Initial velocity = 40 m/s
• Time = 10 seconds

According to the question by using the formula we get,

↦ v = u + at

↦ 0 = 40 + a(10)

↦ 0 = 40 + 10a

↦ - 10a = 40

↦ a = 40/- 10

➠ a = - 4

Hence, the acceleration is - 4 m/s²

As we know that,

• Declaration is the negetive form of acceleration.

∴ The declaration is 4 m/s².

___________________________

(ii) To find the distance travelled by the car,

Given :

• Initial velocity = 40 m/s
• Time = 10 seconds
• Acceleration = 4 m/s

According to the question by using the formula we get,

↦ s = ut + ½at²

↦ s = 40 × 5 + ½ × 4 × (10)²

↦ s = 200 + ½ × (4) × 100

↦ s = 200 + ½ × 400

↦ s = 200 + 200

➠ s = 400 m

∴ The distance travelled by the car is 400 m.