an automobile starts from rest and accelerates to a final velocity in 2 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.
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7.65m/s^2
To find the magnitude of the acceleration in stage 2, we can set up a few equations using the information given.
Let's assume the magnitude of the car's velocity at the end of stage 1 is V1. Since 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, the magnitude of the car's velocity at the end of stage 2 is 2.5V1.
In stage 1, the magnitude of the car's acceleration is given as 3.0 m/s^2. Since the magnitude of acceleration is constant in stage 1, we can use the following equation to find the velocity at the end of stage 1:
V1 = u + a1 * t
Where:
u is the initial velocity (0 m/s since the car starts from rest).
a1 is the magnitude of acceleration in stage 1 (3.0 m/s^2).
t is the time taken in each stage (assumed to be the same for stage 1 and stage 2).
Substituting the values, we get:
V1 = 0 + 3.0 * t
V1 = 3.0t
Now, let's find the velocity at the end of stage 2 using the given information that it is 2.5 times greater than V1:
V2 = 2.5V1
V2 = 2.5(3.0t)
V2 = 7.5t
Since the magnitude of acceleration is given by the rate of change of velocity with respect to time, we can find the magnitude of acceleration in stage 2 using the following equation:
a2 = (V2 - V1) / t
Substituting the values, we get:
a2 = (7.5t - 3.0t) / t
a2 = 4.5t / t
a2 = 4.5 m/s^2
Therefore, the magnitude of the acceleration in stage 2 is 4.5 m/s^2.
To find the magnitude of the acceleration in stage 2, let's break down the problem into steps.
Step 1: Find the velocity at the end of stage 1.
In stage 1, the magnitude of the car's acceleration is given as 3.0 m/s^2. We know that the initial velocity (u) is 0 m/s since the car starts from rest. Let's denote the velocity at the end of stage 1 as v1.
Applying the formula of motion:
v1 = u + (a * t1)
Since the car starts from rest, the formula simplifies to:
v1 = a * t1
Step 2: Find the velocity at the end of stage 2.
According to the problem, 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. Let's denote the velocity at the end of stage 2 as v2.
v2 = 2.5 * v1
Step 3: Find the magnitude of the acceleration in stage 2.
In stage 2, the time taken (t2) is equal to the time taken in stage 1 (t1). Let's denote the magnitude of the acceleration in stage 2 as a2.
Using the formula of motion again, this time for stage 2:
v2 = v1 + (a2 * t2)
Substituting the values we found:
2.5 * v1 = v1 + (a2 * t1)
Simplifying the equation, we get:
1.5 * v1 = a2 * t1
Since both t1 and t2 are equal, we can replace t1 with t2 in the equation:
1.5 * v1 = a2 * t2
Finally, dividing both sides of the equation by t2, we get:
a2 = (1.5 * v1) / t2
Now you can substitute the known values into this equation to find the magnitude of the acceleration in stage 2.