Two particles X and Y starting from rest cover the same distance. The acceleration of X is twice that of Y. The ratio of the time taken by X to that taken by Y is?

Physics Jamb, Waec, Neco Past Questions & Answers on Speed, Velocity and Acceleration

QUESTIONS 50. Two particles X and Y starting from rest cover the same distance. The acceleration of X is twice that of Y. The ratio of the time taken by X to that taken by Y is? 

A. ½ B. 2 C. 1/√2 D.√2 E. 4 

JAMB 1981 Ans: 1/√2 or √½

Solutions 

Parameters

• The Ratio = t(x)/t(y)
• PARTICLE of X
• Acceleration a = 2a = 2

PARTICLE Y

• Acceleration a = a = 1

Using second equation of motion 

S = ut + ½at² for both particles and solving simultaneously 

But ut = 0

Therefore;

S(x) = ½at².........(i)

S(y) = ½at² .........(ii)

S(x) = ½(2a)t².........(ia)

S(y) = ½at² .............(iia)

Assuming a = 1

S(x) = ½(2 x 1)t².........(ib)

S(y) = ½(1)t² .............(iib)

S(x) = ½2t².........(ic)

S(y) = ½t² .............(iic)

But distance of both particles are the same 

Therefore S(x) = S(y) = 1

1 = ½2t².........(id)

1 = ½t² .............(iid)

Making t² the subject of formula 

From (I) t² = 1/½2

t² = 1 x 2/1 x 2

t² = 2/2 

t² = 1

t = √1....................(ie)

From equation (ii) 1 = ½t²

t² = 1/½

t² = 1 x 2/1

t² = 2/1 = 2

t = √2 ......,...............(iie)

Dividing equation (I) by (ii)

t(x)/t(y) = √1/√2 = √1/2 = 1/√2 ANSWER