Question

An object starting from rest travels 20 m in first 2secs. and 160 m in next 4 sec.

Answer 1

An object starting from rest travels 2m in the first 2 seconds and 160m in the next 4 seconds. What will be the velocity after 7 seconds?

I can't tell you the velocity after 7 seconds, since the body is accelerating, the velocity won't be a constant, it changes at every instant of time.

But I can tell you the velocity at 7th second.

The below figure describes the situation,

Let us call velocity at 2s as V1, at 6s as V2 and 7s V3 for our convenience.

x = +1/2 as a * t ^ 2

x = displacement

u = initial velocity

t = time taken

a = acceleration

Now,

For the first 2 seconds,

2 = (0)*(2) + 1/2 * (a)(2*2)

2 = 2 a

a1 = 1m/s^2 (let us call this a1)

V1 = u + (a1)*t

V1 = 2m/s

For the next 4 seconds.

160 = (V1) (4) + (1/2) (a) (4 * 4)

160 = (2)(4) + (1/2)(a)(16)

20 = 1+ a

a2 = 19 m/s^2.(let us call this a2)

Now V2

V2 = V1 + a2 * t

V2 = 2 + (19)(4)

V2 = 38 m/s.

Now our intention is to find V3, at 7th second.

If the object is to move at an acceleration a2 then velocity, V3 is

V3 = V2 + (a2)*(t)

V3 = 38 + 19

V3 = 56 m/s. Is the velocity at 7th second.

Hope it helps…!!!