Question

Two cars (A) and (B) travel in straight line . The distance of (A) from the starting point is given as a function of time be ` a_A (t) = pt + qt^2 `, with ` p = 2 . 60 ms^(-1)` and ` q= 1.20 ms^(-2)`. The distance of (B) from the starting pint is ` x_B (t) = rt^2 - st^3 ` are ` r= 2. 80 ms^(-2)` and ` s = 0.20 ms^(-3)`. Answer the following questions ,
Which car is ahead just after they have the starting point ?
A. ` Car (A) moves ahead `
B. Car (B) moves ahead
C. Cars (A) and (B) move simultaneously
D. Data is insufficient to decide.

Answer 1

Correct Answer - A
` x_A= pt + qt^2 , x_b =rt^2 - st^3`
Velocity, ` v_A= (dx)_A)/(dt) = p+ 2 qt`
` v_B = (dx_B)/(dt) = 2 rt - 3 st^2`
Acceleration, ` a_A = (dv_A)/(dt) = 2 q , a_B= 2 r- 6 st`
The car that initially moves ahead is the one which bas largr velocity at ` t= 0. at ` t=0 , v= p` and ` v_B =0`.
So, initially car (A) moves ahead.