An object moving with uniform acceleration has a velocity of 13.0 cm/s in the positive x-direction when its x-coordinate is 2.73 cm. If its x-coordinate 2.95 s later is −5.00 cm, what is its acceleration? cm/s^2
Express the position of the object in one-dimensional motion at constant acceleration as a function of time. Use the value of the expression at the two times to find the acceleration.
d = 1/2 a t^2 + v0 t + d0
-5.00 = 1/2 a 2.95^2 + 13.0(2.95) + 2.73
To find the object's acceleration, we can use the kinematic equation for position:
x = x0 + v0t + (1/2)at^2
Where:
x = final position
x0 = initial position
v0 = initial velocity
t = time
a = acceleration
Given:
x0 = 2.73 cm
v0 = 13.0 cm/s
x = -5.00 cm
t = 2.95 s
Using the equation, we can substitute the given values:
-5.00 cm = 2.73 cm + (13.0 cm/s)(2.95 s) + (1/2)a(2.95 s)^2
Simplifying the equation:
-5.00 cm = 2.73 cm + 38.35 cm + 4.425a
Rearranging the equation:
4.425a = -5.00 cm - 2.73 cm - 38.35 cm
Calculating:
4.425a = -46.08 cm
Finally, solving for acceleration:
a = (-46.08 cm) / 4.425
a ≈ -10.41 cm/s^2
Therefore, the object's acceleration is approximately -10.41 cm/s^2.
To find the acceleration of the object, we can use the one-dimensional motion equation with constant acceleration:
x = x₀ + v₀t + 0.5at²
Where:
- x is the final position of the object
- x₀ is the initial position of the object
- v₀ is the initial velocity of the object
- t is the time taken
- a is the acceleration
Given information:
x₀ = 2.73 cm
v₀ = 13.0 cm/s
x = -5.00 cm
t = 2.95 s
We can rearrange the equation to solve for the acceleration (a):
a = (x - x₀ - v₀t) / (0.5t²)
Now we can substitute the given values into the equation:
a = (-5.00 cm - 2.73 cm - 13.0 cm/s * 2.95 s) / (0.5 * (2.95 s)²)
Simplifying the equation gives us:
a = (-5.00 cm - 2.73 cm - 38.35 cm) / (0.5 * 8.7025 s²)
a = (-46.08 cm) / 4.35125 s²
To convert cm to m and s² to m²:
a = (-0.4608 m) / 0.0435125 m²
a ≈ -10.58 m/s²
Therefore, the acceleration of the object is approximately -10.58 m/s².
V1 = 13cm/s.
V2 = d/t = (-5-2.73)/2.95 = -2.62cm/s.
Acceleration = the change in velocity / Time to make the change:
a = (V2-V1)/t = (-2.62-13)/2.95 =