Question
Physics Question on Motion in a straight line
A car accelerates from rest at constant rate for first 10s and covers a distance x. It covers a distance y in next 10s at the same acceleration. Which of the following is true?
A
x = 3y
B
y = 3x
C
x = y
D
y = 2x
Answer
y = 3x
Explanation
Solution
Since car accelerates from rest initial velocity is zero. From equation of motion, we have s=ut+21at2 where u is initial velocity, t is time and a is acceleration. Since car accelerates from rest u=0,t=10s ∴s=0+21×a×(10)2=50a..(i) Also, v=u+at where, v is final velocity. ∴ Velocity after 10s is v=0+a×10 v=10a=10×50s..(ii) In the next 10s car moves with constant acceleration and with initial velocity v. ∴s′=vt+21at2 =50s×10×10+21×50s×100=3s Given, s=x and s′=y ∴y=3x