A body moving with uniform acceleration has a velocity of 9.8 cm/s when its x coordinate is 1.38 cm. If its x coordinate 1.4 s later is -8.1 cm, what is the magnitude of its acceleration? Answer in units of cm/s2
To find the magnitude of acceleration, we can use the equation of motion that relates displacement, initial velocity, time, and acceleration:
x = x0 + v0t + (1/2)at^2
where:
x = final position
x0 = initial position
v0 = initial velocity
t = time
a = acceleration
Given:
Initial velocity (v0) = 9.8 cm/s
Initial position (x0) = 1.38 cm
Final position (x) = -8.1 cm
Time (t) = 1.4 s
We can use the equation to solve for acceleration (a).
First, let's rearrange the equation to isolate the acceleration term:
x - x0 = v0t + (1/2)at^2
Now substitute the values into the equation:
-8.1 cm - 1.38 cm = 9.8 cm/s * 1.4 s + (1/2) * a * (1.4 s)^2
-9.48 cm = 13.72 cm/s + (0.7 s^2)a
Let's isolate the acceleration term:
0.7 s^2 * a = -23.2 cm/s - 9.48 cm
0.7 s^2 * a = -32.68 cm/s
Finally, divide both sides of the equation by 0.7 s^2 to solve for the acceleration (a):
a = -32.68 cm/s / 0.7 s^2
a ≈ -46.69 cm/s^2
Therefore, the magnitude of the acceleration is approximately 46.69 cm/s^2.
To find the magnitude of the acceleration, we can use the kinematic equation that relates displacement, initial velocity, time, and acceleration:
x = x0 + v0t + (1/2)at^2
Where:
x = Final displacement
x0 = Initial displacement
v0 = Initial velocity
t = Time
a = Acceleration
Given:
x0 = 1.38 cm (Initial position)
v0 = 9.8 cm/s (Initial velocity)
x = -8.1 cm (Final position)
t = 1.4 s (Time elapsed)
We can rearrange the equation to solve for acceleration:
a = (2(x - x0 - v0t)) / t^2
Now, substitute the given values:
a = (2((-8.1) - 1.38 - (9.8)(1.4))) / (1.4)^2
Simplifying the equation gives:
a = (2(-8.1 - 1.38 - 13.72)) / 1.96
a = (2(-23.20)) / 1.96
a = -45.42 / 1.96
a ≈ -23.18 cm/s^2
Therefore, the magnitude of the acceleration is approximately 23.18 cm/s^2.
d = Vo + 0.5at^2.
d=9.8 + 0.5a(1.4)^2=-8.1 -1.38 = -9.48,
9.8 + 0.98a = -9.48,
0.98a = -9.48 - 9.8 = -19.28,
a = -19.7cm/s^2.
correction: d = Vo*t + 0.5at^2.
9.8*1.4 + 0.5*a(1.4)^2 = -8.1 -1.38,
13.72 + 0.98a = -9.48,
0.98a = -9.48 -13.72 = -23.2,
a = -23.7cm/s^2.