Experiment 2: Uniformly Accelerated Motion — Worked Examples

A trolley is released from rest and travels $0.800\,\text{m}$ in $1.60\,\text{s}$. Assuming constant acceleration, determine $a$.

A best-fit line of distance $d$ versus $t^2$ has slope $0.318\,\text{m/s}^2$. Determine the trolley acceleration.

The trolley position changes from $0.30\,\text{m}$ at $0.95\,\text{s}$ to $0.62\,\text{m}$ at $1.35\,\text{s}$. Determine the average velocity.

Using $a=0.636\,\text{m/s}^2$ and release from rest, determine the instantaneous velocity at $t=1.50\,\text{s}$.

A best-fit velocity-time line passes through $(0.40\,\text{s},0.23\,\text{m/s})$ and $(1.60\,\text{s},0.98\,\text{m/s})$. Determine the acceleration.

A rail is inclined at $4.0^\circ$. Neglecting rolling resistance, predict the along-track acceleration $g\sin\theta$. If the measured value is $0.625\,\text{m/s}^2$, determine the shortfall relative to the ideal prediction. Use $g=9.80665\,\text{m/s}^2$.

A linear fit of $d$ versus $t^2$ gives a nonzero intercept, while a fit of $d$ versus $t$ over the earliest measurements suggests the trolley already had forward velocity at release. Explain how the governing equation changes.

For fixed distance, $a=2d/t^2$. A true travel time is $1.60\,\text{s}$, but a reaction-time delay produces a recorded value of $1.62\,\text{s}$. Determine the ratio of the calculated acceleration to the true acceleration.