# Projectile Motion equations

I did a practicle to show the path of a projectile by rolling a ball down a slope. The graph produced was exponential. The time (tics, time intervals), vertical distance (from starting position) and speed (distance/time) were calculated.

1. Draw a graph of speed vs time (time on x, speed on y)
It produced a straight line. It then asked what this indicates about projectile motion, and how does it correlate with the equations used for projectile motion.
I said that v is proportional to t, as when time increases, so does velocity. I used the equation v = u + at, where u = 0, and a can be gravity, so v = 9.8t ... so v increases at a constant rate. Would this be correct?

2. Draw the graph of vertical distance vs time (time on x, distance on y). It produced an exponential, with the curve increasing upwards as x increases.It then asked what this indicates about projectile motion, and how does it correlate with the equations used for projectile motion.
I said that d is inversely proportional to t, as when t increases, d does in a non-linear fashion. I need help finding an equation for this though.

3. Draw a graph of distance vs t^2 (t^2 on x, d on y). It produced a straight line. It asks to explain the meaning of the graph, so i used s=ut+0.5at^2, u = 0, so s = at^2, so as time increases, so does distance... would this be correct?

Any help or advice given would be GREATLY appreciated
Thanks in advance

## Answers and Replies

Redbelly98
Staff Emeritus
Science Advisor
Homework Helper
Welcome to Physics Forums.
I did a practicle to show the path of a projectile by rolling a ball down a slope. The graph produced was exponential. The time (tics, time intervals), vertical distance (from starting position) and speed (distance/time) were calculated.

1. Draw a graph of speed vs time (time on x, speed on y)
It produced a straight line. It then asked what this indicates about projectile motion, and how does it correlate with the equations used for projectile motion.
I said that v is proportional to t, as when time increases, so does velocity. I used the equation v = u + at, where u = 0, and a can be gravity, so v = 9.8t ... so v increases at a constant rate. Would this be correct?
Pretty much, though if the object was rolling down an incline then a won't be 9.8 m/s2. You can figure out what a is by getting the slope of the v-vs-t graph.
2. Draw the graph of vertical distance vs time (time on x, distance on y). It produced an exponential, with the curve increasing upwards as x increases.It then asked what this indicates about projectile motion, and how does it correlate with the equations used for projectile motion.
I said that d is inversely proportional to t, as when t increases, d does in a non-linear fashion. I need help finding an equation for this though.
You already have the equation, it's the "s=ut+0.5at^2" that you give below. Note, this is neither an exponential nor an inverse proportion, but it is a type of equation you would have studied in algebra.
3. Draw a graph of distance vs t^2 (t^2 on x, d on y). It produced a straight line. It asks to explain the meaning of the graph, so i used s=ut+0.5at^2, u = 0, so s = at^2, so as time increases, so does distance... would this be correct?
It's correct, but your teacher might be looking for more than that. I'm a little puzzled by the phrase "explain the meaning of the graph", is that the exact wording of the question?