An object starts from rest an undergoes a constant acceleration in the positive x direction. After some time it covers a displacement of 37 meters in the positive x direction achieving some final velocity. If the object started from rest with double the original acceleration (acceleration is constant again) and then got of to a final velocity which is a factor of 2.3 larger than the original final velocity, what is the magnitude of the new displacement in meters? Hint: Use an appropriate constant acceleration equation and use proportions.

Question

An object starts from rest an undergoes a constant acceleration in the positive x direction. After some time it covers a displacement of 37 meters in the positive x direction achieving some final velocity. If the object started from rest with double the original acceleration (acceleration is constant again) and then got of to a final velocity which is a factor of 2.3 larger than the original final velocity, what is the magnitude of the new displacement in meters? Hint: Use an appropriate constant acceleration equation and use proportions.

Answer 1

original acceleration is a

1/2 at^2 = 37
v = at

new acceleration is 2a
since v = 2at, new time is (2.3v)/(2a) = 2.3at/2a = 1.15t

new displacement is

1/2 (2a)*(1.15t)^2 = 2*1.15^2 at^2 = 5.29*37 = 195.73 m

Answer 2

To solve this problem, we can use the equation for displacement (x) given constant acceleration (a) and final velocity (v):

x = (v^2 - u^2) / (2a),

where u is the initial velocity (which is 0 in this case).

Let's call the original acceleration a1, the original final velocity v1, and the magnitude of the new displacement x2.

For the first scenario:
Acceleration (a1) = a
Final velocity (v1) = v

Using the given information, we have:
x1 = 37 meters

Using the equation for displacement, we can rearrange it to find v in terms of x and a:

v1 = √(2a1x1).

Now, let's consider the second scenario:
Acceleration (a2) = 2a1 (double the original acceleration)
Final velocity (v2) = 2.3v1 (2.3 times the original final velocity)

We want to find the magnitude of the new displacement (x2).

Using the equation for displacement, we can rearrange it to find x in terms of v and a:

x2 = (v2^2 - u^2) / (2a2).

Since the initial velocity (u) is 0, the equation becomes:

x2 = v2^2 / (2a2).

Substituting the given values:
a2 = 2a1
v2 = 2.3v1

We can rewrite the equation for x2 as:

x2 = (2.3v1)^2 / (2*2a1).

Simplifying further:
x2 = (2.3^2 * v1^2) / (4a1).
x2 = (5.29 * v1^2) / (4a1).

To find x2, we need to substitute the values of v1 and a1 into this equation. However, the values of v1 and a1 are not provided in the question. Therefore, we need additional information or values to compute the magnitude of the new displacement, x2.