My Math Forum Finding acceleration through distance and time?

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 October 1st, 2017, 03:35 PM #1 Newbie   Joined: Oct 2017 From: England Posts: 1 Thanks: 0 Finding acceleration through distance and time? I’ve been presented with a question in my assignment and have no idea have to solve it. “A particle is moving along a straight line with constant acceleration. It passes through points A, B and C. It takes 2 secs to travel from A to B, a distance of 14 m, and takes 3 secs to travel from B to C, a distance of 36m. Find the acceleration of the particle, and the speed as it passes through point A.” I do not know how to calculate acceleration with only speed/ velocity and distance/ displacement.
October 1st, 2017, 04:31 PM   #2
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Quote:
 “A particle is moving along a straight line with constant acceleration. It passes through points A, B and C. It takes 2 secs to travel from A to B, a distance of 14 m, and takes 3 secs to travel from B to C, a distance of 36m. Find the acceleration of the particle, and the speed as it passes through point A.”
using the kinematics equation, $\Delta x = v_0 \cdot t + \dfrac{1}{2}at^2$

A to B ...

$\Delta x = 14 \, m$, $\Delta t = 2 \sec$

$\color{red}{7 = v_0 + a}$

A to C ...

$\Delta x = 50 \, m$, $\Delta t = 5 \sec$

$\color{red}{20 = 2v_0 + 5a}$

solve the $\color{red}{system}$ of equations for $v_0$ and $a$

October 2nd, 2017, 06:38 AM   #3
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Quote:
 Originally Posted by Spacetrum I’ve been presented with a question in my assignment and have no idea have to solve it. “A particle is moving along a straight line with constant acceleration. It passes through points A, B and C. It takes 2 secs to travel from A to B, a distance of 14 m, and takes 3 secs to travel from B to C, a distance of 36m. Find the acceleration of the particle, and the speed as it passes through point A.” I do not know how to calculate acceleration with only speed/ velocity and distance/ displacement.
Just for the record, you're only able to calculate acceleration here because you have three points which describe points in a trajectory (displacement and time). That allows you to get two average velocities over the two intervals between points 1 to 2 and 2 to 3. Consequently, the average change in velocity can be determined and therefore the average acceleration over the whole interval.

If you only had two data points for the trajectory, you wouldn't be able to estimate the acceleration.

 Tags acceleration, distance, finding, mechanics, time

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