Kinematics Problem-solving session

Links and useful resources

Lightning Round Questions

What is PWM and what are some common uses for it?
(lang) What is a clause?
If the surface of the moon is covered in fine, sandy material, why are there no dunes on the moon?
Explain what impulse is.
gr7 lightning points: [lightning:: 4]
gr10 lightning: [lightning:: 1]

Lesson content with examples

Kinematic Equations Recap

These equations will get you a long way toward finding the solution for most problems with constant acceleration:

$x = \frac{1}{2} a t^{2} + v_{0} t + x_{0}$
$v = a t + v_{0} t$

variable	interpretation
$x$	position, or displacement from whatever your starting point is
$t$	Time since the start of the period of time we're working with
$v$	Velocity at the current moment (determined by your choice of a value for $t$
$v_{0}$	The initial velocity (velocity we had going into the problem)
$x_{0}$	The initial position (location relative to our zero point at the start of the problem)

Notice that position is always a parabolic curve if you have constant acceleration (even if the acceleration is in the opposite direction of the initial velocity). With constant acceleration, velocity changes linearly.

BE CAREFUL: there are many situations in which acceleration is not constant. These equations will not work if the acceleration changes during the time covered by the equation. You can still use them, but only if you can break the time segments into pieces in which the acceleration is constant. Otherwise, you're going to need more math powertools (calculus).

Problem-solving tips

If you need to know the maximum (or minimum) position, that means that the object reversed direction at that same moment (otherwise, it wouldn't be the max because it kept going even farther...). When it reverses direction, the sign of its velocity has to change, and that means that its velocity was zero in the direction of the acceleration at that moment. You can find that moment by solving the velocity equation for the time when it's zero, and then use the result to calculate what the position was at that time.
The acceleration at any moment is always equal to the slope of the velocity graph at that moment
The velocity at any moment is always equal to the slope of the position graph at that moment
Average velocity is often useful in problems with constant acceleration, because you can use it to calculate distance traveled without using the full kinematic equation

Media resources

Youtube search for "solving kinematic equations for the different unknowns"

Guided practice

find the dot product: $4 \hat{i} + 3 \hat{j} - 2 \hat{k} \cdot \frac{1}{2} \hat{i} - \frac{2}{3} \hat{j} + \hat{k}$
find the vector magnitude of $5 \hat{i} - 12 \hat{j} + 13 \hat{k}$
How far will a rock fall in 10 seconds if dropped in Earth's gravity?
How high will a bullet go if shot straight up at an initial velocity of 1000 ft/sec?
How far does a frog leap if it extends its legs by 15 cm during a 65 ms pushoff at a 30 $°$ angle?
A plane is flying at 500 mph in a due-east heading, but the pilot doesn't know that there is a 50 mph wind blowing to the south. What is the plane's actual ground speed? If the plane flies for 36 minutes, how far south of its expected position will it actually end up?

Homework

#hw (physics) In the plane problem we did in class (click here to see the question), in what direction should the pilot orient the plane in order to compensate for the wind and end up at his desired location? Give the direction as an angle from due east.
#hw (physics) A ball thrown horizontally at 25 m/s travels a horizontal distance of 50m before hitting the ground. How high was it above the ground when it was thrown?
#hw (physics) A rifle is fired horizontally at a target 50m away. The bullet hits the target 2.0 cm below the aim point. What was the bullet's flight time? What was the bullet's speed just as it left the barrel?