Question

A particle starts from the origin at t=0 with a velocity of 10 j m/s and moves in the xy plane wid a constant acceleration of 8 i + 2j ms-2. (i) at what time is the x-coordinate of the particle 16m? what is y-coordinate of the particle at the time. (ii) what is the speed of the particle at that time.

Answer 1

A body starts from rest means initial velocity is 0 m/s and travelling with an acceleration of 4 m/s².

We have to find the distance travelled by the body in the 4th second.

We know that distance covered by body in nth second is given by-

Sn = u + a/2 (2n - 1)

Here; n = 4 sec, u = 0 m/s and a is 4 m/s².

Let us assume that the distance covered in the 4th second is x km.

Substitute the known values in the above formula,

→ x = 0 + 4/2 (2*4 - 1)

→ x = 0 + 2 (8 - 1)

→ x = 0 + 2(7)

→ x = 0 + 14

→ x = 14

As, the x is the distance covered in 4th second.

Therefore, the distance covered by the body in the 4th second is 14 m.