Magnitude of acceleration??? This question is driving me nuts.?

Question

A car starts from rest and accelerates to a final velocity in two stages along a straight road. Each stage occupies the same amount of time. In stage 1, the magnitude of the car's acceleration is 3.0m/s^2. The magnitude of the car's velocity at the end of stage 2 is 2.5 times greater than it is at the end of stage 1. Find the magnitude of the acceleration in stage 2.

Answer 1

Stage 1: V1 = at = 3t
with V1 = end velocity after stage 1 and t = time

Stage 2:
V2 = start velocity + at
= V1 + at
= 3t + at
We also know that
V2 = 2.5 V1
= 7.5 t

=> 7.5 t = 3t + at
=> a = 4.5 m/s^2

Answer 2

The trick here is the magnitude means plus or minus. The magnitude of +3 is the same as the magnitude of -3.

Lets call the acceleration and final velocity for stage 1, a1 and v1.
Lets call the acceleration and final velocity for stage 2, a2 and v2.
Lets call the time in each stage T

Then a1 = 3, and v1 = 3T.
v2 = v1 + (a2) T.
And we're told that Mag(v2) = 2.5 Mag(v1), which means that
v2 = (+ or -) 2.5 v1.
So then we get:
(+ or -)2.5 v1 = v1 +(a2) T
Substitute for v1:
(+ or -) 2.5 (3T) = 3T +(a2) T
Divide by T
(+/-)7.5 = 3 + a2
Subtract 3 from each side
(+/-)7.5 -3 = a2
So a2 is either one of these:
+7.5 - 3 = +4.5, or
- 7.5 - 3 = -10.5.

To make this more specific, lets try the case where the time is 1 second for each stage. Then the velocity at the end of stage 1 is 3 m/s. The velocity at the end of stage 2 is either +7.5 m/s, or -7.5 m/s.

Answer 3

Intuitively you would assume that the acceleration would be 2.5 times greater also. Which it is.

To prove it, do the calc.

We know v = at. We know the time, t is equal for each stage.

So Vo = 3t for state 1. Vf = 2.5Vo = a t

Solve each for t. t = Vo/3 and t = 2.5Vo/a

Set them equal to each other. Vo/3 = 2.5Vo/a

The Vo's cancel, thus 1/3 = 2.5/a

a = 2.5 * 3 = 7.5

ANSWER ====> a = 7.5 m/s/s

Answer 4

7.5m/s^2

if u substitute in numbers, lets say for each stage, the time was 2 seconds, in the first stage, u get 6m/s. So, for the second stage, ur velocity is 2.5 x 6, which is 15m/s. Divide that by 2, and u get 7.5m/s^2