Comparing motion of two objects problem

[angmokio]

Motion problem!

1. Objects A and B both start from rest. They both accelerate at the same rate. However, object A accelerates for twice the time as object B. What is the distance traveled by object A compared to that of object B?


2. V_f = V_o + at, X - X_o = V_ot + 1/2at², V²= V_o² + 2a(X - Xo)


3. 2a_A= a_B
=> V_Ao² + 4a(X - Xo) = V_Bo² + 2a(X - Xo)
=> distance traveled by object A four times as far of object B??

Am i correct?

 

[method_man]

They both accelerate at the same rate. However, object A accelerates for twice the time as object B.
3. 2a_A= a_B

Shouldn't be t_a=2t_b?

 

[willem2]

=> distance traveled by object A four times as far of object B??

Am i correct?

yes, the distance traveled by A at the time A stops accelerating is 4 times the distance
traveled by B at the time B stops accelerating.

I can't see how you get there however. you never use the fact that the time that a
accelerates is twice as long. I think it's easiest to use x = v_0 t + (1/2) a t^2, and

substitue t_A = T and t_B = 2T in it