Question

Two scooters starting from rest accelerate uniformly at the same rate. The second scooter travels twice the time of the first scooter. Then, the relation between the distance covered by the first scooter (S1) to that of second scooter (S2) is

Answer 1

Answer:

2S2=S1

as S2 travels twice distance of s1 in the same time.

let us consider that both takes time x to reach at point b from a.

so by the given condition in the time s1 covers some distance(d) s2 will cover distance (2d) in same time

Answer 2

Answer will be S2 = 4(S1)

Let 'u' be the initial velocity, t be the time taken, 'a' is the acceleration and 'S' is the distance covered.

Using the second equation of motion

$s = ut + \frac{1}{2} a {t}^{2}$

,(u=0, since it starts from rest).

⇒

$s = \frac{1}{2} a {t}^{2}$

Since, 'a' is constant,

S ∝ t²

Let

S1

be the distance covered by the first scooter and

S2

be the distance covered by the second scooter.

Let

t1

be the time taken by the first scooter and

t2

be the time taken by the second scooter.

According to the question,

t2 = 2(t1)

Then,

$\frac{S1}{S2} = \frac{t1²}{t2²}$

or,

$\frac{S1}{S2} = \frac{t1²}{(2t1)²}$

⇒$\frac{S1}{S2} = \frac{t1²}{4t1²}$

or,

S2=4S1