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 3.3 m/s2. The magnitude of the car's velocity at the end of stage 2 is 2.0 times greater than it is at the end of stage 1. Find the magnitude of the acceleration in stage 2.
To find the magnitude of the acceleration in stage 2, we can follow these steps:
Step 1: Assign variables
Let's assign variables to the given information:
- The magnitude of acceleration in stage 1: a1 = 3.3 m/s^2
- The magnitude of velocity at the end of stage 1: v1
- The magnitude of velocity at the end of stage 2: v2
Step 2: Define relationships
We're given that each stage occupies the same amount of time, so we can assume that the time taken in each stage is equal. Let's call this time t.
Since the final velocity at the end of stage 2 is 2.0 times greater than it is at the end of stage 1, we can express this relationship mathematically:
v2 = 2 * v1
Step 3: Use kinematic equations
We can use the equations of motion to relate the variables. In this case, we'll use the equation:
v2 = v1 + a2 * t
where a2 is the magnitude of acceleration in stage 2.
Step 4: Solve for a2
Substitute the given information into the equation:
2 * v1 = v1 + a2 * t
Rearrange the equation:
v1 = a2 * t
Solve for a2:
a2 = v1 / t
Step 5: Substitute values and calculate
Since the information doesn't provide specific values for v1 or t, we can't determine the exact magnitude of the acceleration in stage 2. However, we can calculate it using the given ratio.
Given the ratio between v2 and v1 is 2.0, we can substitute v2 = 2 * v1 into the equation and simplify:
a2 = v1 / t
= v2 / (2 * t)
= (2 * v1) / (2 * t)
= v1 / t
So, the magnitude of the acceleration in stage 2 is the same as the magnitude of the acceleration in stage 1, which is 3.3 m/s^2.