Question

A dog initally running at a velocity of 2m/s, accelerates at a constant rate of 1.5m/s-2 for 5s.Calculate .
1.The distance covered by the dog form the initial position.
2. The final velocity in kmh-1

Answer 1

Question :-

A dog initally running at a velocity of 2 m/s accelerates at a constant rate of 1.5 m/s² for 5s. Calculate -

i) The distance covered by the dog form the initial position.

ii) The final velocity in km/h

Answer :-

Given :-

• Initial velocity = 2 m/s
• Acceleration = 1.5 m/s²
• Time = 5 seconds

To Find :-

• Distance covered
• Final velocity ( in km/h )

Solution :-

Firstly, Calculating distance covered -

Here, we are given initial velocity, acceleration and time, so by simply substituting the value in 2nd equation of motion, we can find distance travelled -

⇒ s = ut + ½ at²

⇒ s = 2 × 5 + ½ × 1.5 × 5 × 5

⇒ s = 10 + ½ × 37.5

⇒ s = 10 + 18.75

⇒ s = 28.75

Distance travelled = 28.75 m

Calculating final velocity :-

Substituting the value in 1st equation of motion -

⇒ v = u + at

⇒ v = 2 + 1.5 × 5

⇒ v = 2 + 7.5

⇒ v = 9.5 m/s

Final velocity = 9.5 m/s

Here, we are asked velocity in km/h, so now we need to convert it to m/s -

To convert m/s to km/h simply multiply by 5/18 :-

9.5 × 5/18 ≈ 2.6

Final velocity = 2.6 km/h

Answer 2

Given :

Initial velocity of the dog = 2 m/s

Acceleration of the dog = 1.5 m/s²

Time taken = 5 sec

To Find :

(a) Distance covered by the dog from the initial position.

(b) Final velocity of the dog

Solution :

(a) As we are provided with initial velocity, acceleration and time we can use second equation of kinematics that is

s = ut + 1/2 at²

here, s denotes distance covered, u denotes initial velocity t denotes time taken and a denotes acceleration.

By substituting all the given values in the formula,

➙ s = ut + 1/2 at²

➙ s = 2 × 5 + 1/2(1.5)(5)²

➙ s = 10 + 1/2(37.5)

➙ s = 10 + 18.75

➙ s = 28.75 m.

Thus, the distance covered by the dog from initial position is 28.75m.

(b) Here, we can use first equation of kinematics that is,

v = u + at

by substituting all the given values in the equation,

➙ v = u + at

➙ v = 2 + (1.5)(5)

➙ v = 2 + 7.5

➙ v = 9.5 m/s

We know that,

5/18 m/s = 1 km/hr

9.5 m/s = 9.5 × 5/18 = 2.6 km/hr

Thus, final velocity of the dog is 2.6 km/hr.

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