Question

22. The displacement of a particle is given by x = (t-2) where all quantities are
in SI units. What is the distance covered by the particle in first 4 seconds? ​

Answer 1

Correct Question :

The displacement of a particle is given by x = (t-2)² where all quantities are in SI units. What is the distance covered by the particle in first 4 seconds?

Answer :

Displacement of the particle = x = (t-2)² m.

Now, differentiating :

⇒ (t - 2)²

⇒ 2(t - 2)

⇒ 2t - 4

Now,

Let's find : The Displacement when t = 0.

⇒ 2t - 4

⇒ 2*0 - 4

⇒ 0 - 4

⇒ - 4 m

Now, The Displacement when t = 2.

⇒ 2t - 4

⇒ 2*2 - 4

⇒ 4 - 4

⇒ 0 m

And, The Displacement when t = 4.

⇒ 2t - 4

⇒ 2*4 - 4

⇒ 8 - 4

⇒ 4 m

Now, we know that the distance travelled is the area under the slope.

Hence, let's find the area -

⇒ ½*2*4 + ½*2*4

⇒ 4 + 4

⇒ 8 metres

Hence, The distance travelled by the particle is 8 m.