Question

MULTIPLE ANSWER QUESTION

the ratio of time taken by two cars P,Q starting from rest moving along a straight road with equal accelerations is √2 : 1 , THEN THE:

a)final velocity of car P > final velocity of car Q
b)final velocity of car P < final velocity of car Q
c)ratio of Vp to Vq is 2 : √2
d)ratio of distance travelled by car 'P' to car 'Q' is 2:1

Answer 1

Since it is given that acceleration is same: a₁=a₂

we know the acceleration formula: a=(v-u)/t
a=acceleration         v=final velocity
u=initial velocity       t=time taken

since it starts from rest u=0

Acceleration for P: 
a₁=Vp/t₁       (u=0)

Acceleration for Q:
a₂=Vq/t₂  (u=0)

Since given acceleration same: a₁=a₂
∴a=  Vp/t₁  =  Vq/t₂

        Vp/Vq = t₁/t₂

given tht t₁/t₂=√2/1

So Vp/Vq= √2/1...........................(1)
Well √2/1 is not in the option, But it is same as    2/√2= √2/1 option (c)

Form this we can also get that Velocity of P> velocty of Q ,so (a) is also right answer


Now, considering Distance:
Distance=velocity×time
(since we have only ratios,we cant take it as the same hence,we put a variable x)
 
From (1) we got velocity of p=√2 x
                          velocity of q=1 x

Given that time taken by p= √2 x
                  time taken by q=1 x

Distance traveled by P= √2×√2=2x²
Distance travelled by Q= 1×1=1x²

Distance travelled byP/Distance travelled by Q=2x²/1x² =2:1 (x² gets canceled)
So answer (D) is right



So the answer is option  (a) ,(c) and (d)