Question

A car, starting from rest, has a constant acceleration a1 for a time interval t1 during which it covers a distances s1 . In the next time interval t2, the car has a constant retardation a2 and comes to rest after covering a distance s2 in time t2

Answer 1

Answer:

here is the answer hope it helps

Answer 2

To find : which of the following relations is correct ?

solution : case 1 : A car, staring from rest, has a constant acceleration a₁ for a time interval t₁ during which it covers s₁ distance.

so, initial velocity, u = 0

using formula, s = ut + 1/2 at²

s₁ = 1/2a₁t²₁ ...(1)

and velocity after time t₁ , v₁ = a₁t₁

case 2 : in the next interval t₂, the car has a constant retardation a₂ and comes to rest after covering a distance s₂ in time interval t₂.

so, velocity after time t₂, v₂ = u₂ - a₂t₂

here, u₂ = v₁ = a₁t₁

v₂ = a₁t₁ - a₂t₂

but body comes to rest so v₂ = 0

so, a₁t₁ - a₂t₂ = 0

⇒a₁/a₂ = t₂/t₁ ...(2)

now, distance covered in t₂ time, s₂ = 1/2 a₂t₂² ...(3)

from equations (1) and (3),

s₁/s₂ = a₁t₁²/a₂t₂²

from equation (2) we get,

s₁/s₂ = t₁/t₂ ...(4)

from equations (2) and (4) we get,

a₁/a₂ = s₂/s₁ = t₂/t₁

Therefore option (4) is correct choice.