![To find the uniform acceleration, you can use the formula:
\[
a = \frac{{v_f - v_i}}{{t}}
\]
where:
- \( v_f \) is the final velocity (96 m/s)
- \( v_i \) is the initial velocity (36 m/s)
- \( t \) is the time (8.0 s)
Substituting the values:
\[
a = \frac{{96\, \text{m/s} - 36\, \text{m/s}}}{{8.0\, \text{s}}}
\]
\[
a = \frac{{60\, \text{m/s}}}{{8.0\, \text{s}}} = 7.5\, \text{m/s}^2
\]
So, the uniform acceleration is **7.5 m/s²**.](https://theinternetioimages-f2htc2ggcrath6d7.z01.azurefd.net/$web/askai/d3be4378-f711-428b-97b0-cab8a88cc611.webp)
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Question: Find the uniform acceleration that causes a car's velocity to change from 36 m/s to 96 m/s in an 8.0 s period.
To find the uniform acceleration that causes the change in velocity, you can use the formula for acceleration: \[ a = \frac{\Delta v}{\Delta t} \] where: - \( \Delta v \) is the change in velocity, - \( \Delta t \) is the change in time. Given: - Initial velocity, \( v_i = 36 \text{ m/s} \) - Final velocity, \( v_f = 96 \text{ m/s} \) - Time period, \( t = 8.0 \text{ s} \) First, calculate the change in velocity (\( \Delta v \)): \[ \Delta v = v_f - v_i = 96 \text{ m/s} - 36 \text{ m/s} = 60 \text{ m/s} \] Now use the formula for acceleration: \[ a = \frac{\Delta v}{\Delta t} = \frac{60 \text{ m/s}}{8.0 \text{ s}} = 7.5 \text{ m/s}^2 \] So, the uniform acceleration is \( 7.5 \text{ m/s}^2 \).
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