An automobile 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 3.5 m/s2. The magnitude of the car's velocity at the end of stage 2 is 2.9 times greater than it is at the end of stage 1. Find the magnitude of the acceleration in stage 2.

STage2:

acceleration= (V2-V1)/T=V1(1.9)/T

Stage1:

acceleration= (V1-0)/T
3.5=V1/T

So we put V1=3.5T in the first equation..
acceleartion= 3.5T*1.9/T= 3.5*1.9 m/s^2

so there you have it.

6.004

To find the magnitude of the acceleration in stage 2, we can start by assigning variables to the given values and using the formula of motion involving acceleration, velocity, time, and displacement.

Let's assume:
- The magnitude of the acceleration in stage 1 is a1.
- The magnitude of the acceleration in stage 2 is a2.
- The initial velocity is v0 (which is at rest, so v0 = 0).
- The final velocity at the end of stage 1 is v1.
- The final velocity at the end of stage 2 is v2.

From the given information, we know that:
- The magnitude of the acceleration in stage 1 (a1) is 3.5 m/s^2.
- The magnitude of the acceleration in stage 2 (a2) is unknown.
- The magnitude of v2 is 2.9 times greater than the magnitude of v1 (v2 = 2.9v1).

Since both stages occupy the same amount of time and the initial velocity is 0, we can determine the final velocities as follows:
- The final velocity at the end of stage 1 (v1) = a1 * t, where t is the common time for both stages.
- The final velocity at the end of stage 2 (v2) = (a1 + a2) * t.

Now, we can use the information about v1 and v2 to set up an equation:
v2 = 2.9v1
(a1 + a2) * t = 2.9 * (a1 * t)

Simplifying the equation, we get:
a1 + a2 = 2.9a1

Next, we substitute the value of a1 (3.5 m/s^2) into the equation:
3.5 + a2 = 2.9 * 3.5

Solving the equation:
3.5 + a2 = 10.15
a2 = 10.15 - 3.5
a2 = 6.65 m/s^2

Therefore, the magnitude of the acceleration in stage 2 is 6.65 m/s^2.