Objects A and B both start at rest. They both accelerate at the same rate. However, object A accelerates for?

Question

twice the time as object B. What is the final speed of object A compared to that of object B?

Answer 1

The change in velocity can be found as the acceleration multiplied by the change in time.
Δv = a * Δt

The final velocity can be found as,
v = V_0 + Δv
The final velocity equals the initial velocity + the change in velocity.

Since both objects start from rest, both of their initial velocities equal zero, so in this case their final velocities equal their changes in velocity.

V_A = a * Δt_A
V_B = a * Δt_B
Where V_A and V_B are the final velocities of objects A and B respectively and Δt_A and Δt_B are the times the object are accelerating.

If Δt_A = 2 * Δt_B, we can plug this secondary equation back into the above equation to get,
V_A = a * (2 * Δt_B)
V_B = a * Δt_B

If we take the ratio of the final speeds,
V_A / V_B = (a * (2 * Δt_B)) / (a * Δt_B)
We get 2.

The final speed of object A is two times greater than the final speed of object B.
V_A = 2 * V_B

Answer 2

there's no longer sufficient suggestions to respond to. you could furnish how long one in each of them sped up for, and to what acceleration and then at what time you pick the dimensions. finally, is the acceleration a promptly line?. Are you asking the area traveled on the top of the time that merchandise A sped up? So, enable's say they have been accelerating 0-60mph in one minute, yet B stops at 30 seconds. A. A will standard 30 miles in step with hour over the minute (on a promptly line) that's a million/2 mile in step with minute=.5 miles B. on the top of a minute B could have long previous 0-30 interior the 1st a million/2 minute(=an standard of 15mph=a million/4 mile in step with minute=a million/8 mile in that 30 seconds)=.a hundred twenty five + 30mph interior the 2d a million/2 min(=a million/2 mile in step with minute=a million/4 mile in that 30 seconds)=.25 for a complete of .375miles SO right here none of your possibilities is authentic

Answer 3

If we calculate the speeds based on variables x=acceleration and t=time then we can find the comparison

speed of b=xt
speed of a=x(2t)=2xt

as you can see, the speed of a is twice that of b if the time is multiplied by 2

Answer 4

Note v(A) or a(A) means v subscript A and a subscript A

dv/dt = a

integration gives:

v = at + c

at t = 0, v=0 (stated in question) so c = 0

v = at

For A : a(A) = 2a

v= 2at

For B a(B) = a

v = at

so final speed of A will be twice that of B

Answer 5

A's speed should be twice as B's speed.

We know that,
dv = a.dt
from the integer we get (assuming the "a" as a constant)
Vo - Vf = a (to - tf)
where,
Vo = initial speed
Vf = final speed
a = acceleration
to = initial time
tf = final time.

for B, we would get:

Vf(B) = a.tf

And A,
Vf(A) = a.(2tf)

In conclusion,

Vf(A)/Vf(B) = 2.

Answer 6

A's speed will 2 times of B.
according to simple equation
velocity = accl * time

Answer 7

twice as much