AP Physics Lap 1 Webassign Explanations

A car is traveling at --- m/s, and the driver sees a traffic light turn red. After --- s (the reaction time), the driver applies the brakes, and the car decelerates at --- m/s2. What is the stopping distance of the car, as measured from the point where the driver first sees the red light?

to solve for this, we have to first find the point where the velocity is zero to find stopping time, so divide the initial velocity (Vi) by the deceleration rate (A). After that, multiply the reaction time (r) by the initial velocity (Vi) and add that to half of the stopping time (st) multiplied by the initial velocity (Vi). We do this because we need to take the velocity vs. time graph and find the area underneath the line to find distance d = (Vi)/(A)*1/2(Vi) + (Vi)*(r)

In reaching her destination, a backpacker walks with an average velocity of --- m/s, due west. This average velocity results because she hikes for 6.44 km with an average velocity of ---m/s, due west, turns around, and hikes with an average velocity of --- m/s, due east. How far east did she walk?

1) get a velocity equation (Va = Da/Ta) (average velocity is change in distance over change in time) and substitute (Ta) for (Da/Va) so we don't have to deal with time Va = (Da/(Da/Va) 2) expand for east and west info Va = (Dw-De)/(Dw-De)/(Vw-Ve) 3) simplify and you get De(Va+Ve)/(V*Ve) = Dw(Vw-Va)/(V*Vw) 4) solve for (De) and you get De = Dw(Ve/Vw)(Vw-Va)/(Ve+Va) 5) now you can plug in ur info and solve for distance traveled east

From her bedroom window a girl drops a water-filled balloon to the ground, x meters below. If the balloon is released from rest, how long is it in the air?

So we're doing a freefall problem, which means that we have a constant acceleration of 9.8 m/s^2, so first we need to take the freefall equation which is (d = Vi + 1/2*a*t^2) so we know acceleration (9.8 m/s^2), distance (x), and initial velocity (0) so solve for time (t = sqrt (2[d-Vi]/a))

A person who walks for exercise produces the position-time graph given below.

a) because this is a distance vs. time graph, the slope is in m/s which means that the slope is the velocity so if the slope is positive, negative, or zero is is the velocity b) to find the average velocity just take the distance per segment and put it over the time per segment (NOT the total time and total distance) --- dont forget to put negative signs if the slope is negative

The St. Charles streetcar in New Orleans starts from rest and has a constant acceleration of --- m/s2 for --- s.

a) draw a velocity vs. time graph, this should start at zero and increase at a constant rate b) the distance at (x) seconds can be found by first solving (c) and finding the velocity at (x) seconds and then finding the area underneath the graph to that point. Because it starts at a speed of zero and a distance of zero, you can just multiply (x) seconds by (c) speed to and divide by two to find distance. (d = 1/2([x]*[c])) c) the speed at (x) seconds can be found by multiplying the acceleration by (x) (if there was an initial velocity you would add it to that but b/c it starts from rest you add zero) d) draw a position vs. time graph, with time starting at zero and increasing in increments of 2 seconds. This graph should look like a y = a^x graph, with the curve increasing in the positive x direction

A dynamite blast at a quarry launches a chunk of rock straight upward, and X s later it is rising at a speed of Y m/s. Assuming air resistance has no effect on the rock, calculate its speed at (a) at launch and (b) Z s after the launch. at launch

a) okay so we're looking for initial velocity which means that we can backtrack from the point they gave us. Because its going into the air, we have a negative gravitational pull, so take the point we have lets say (x seconds, y m/s) and multiply x by 10 m/s (gravity) (we do this to find the velocity that was lost due to gravity) then add that to y m/s to find the initial velocity (9.8*x + y = Vi) b) to find what happens at z we have to do the same thing, multiply z by -9.8 m/s (because now were going the right direction and not retracing what already happened) and add that to the initial velocity, if it creates a negative number that we know that it has already reached its peak and is on its way back towards the ground, so get rid of the negative sign and there's your answer (Vi - 9.8*z)

Given the quantities A, B, and C, what is the value of the quantity d = a3/(cb2)?

a) plug the quantities into the equation d = a3/(cb2) and solve b) plug the UNITS into the equation and solve (a = meters, b = seconds, c = meters/seconds) d = m^3/(m/s)*s^2 d = m^3/m*s d = m^2/s

A train, traveling at a constant speed of -- m/s, comes to an incline with a constant slope. While going up the incline, the train slows down with a constant acceleration of magnitude -- m/s2.

a) so graph a velocity vs. time graph this should be a straight line b/c it has a constant acceleration, it should start at the initial velocity and steadily decrease b) to find the speed after (x) seconds, multiply the acceleration by the seconds and then subtract from the initial velocity (constant speed) (we do this because if it's decreasing at a constant rate every second, then every second you subtract the deceleration so by multiplying and then subtracting you get the answer) c) to find the distance after (x) seconds, take the velocity vs. time graph from (a) and find the area under the portion from zero seconds and the initial velocity to (x) seconds and the velocity you found in answer (b) d = 1/2*([x] - 0)/([b] - [Vi]) d) draw a distance vs. time graph with the time starting at zero and increasing by two seconds each interval. This should look like a y = a^x graph, where it curves in the positive x direction

One afternoon, a couple walks three-fourths of the way around a circular lake, the radius of which is ---- km. They start at the west side of the lake and head due south to begin with.

a) to find total distance, we have to find 3/4 of the circumference which is (C = 3/4 *2πr) b1) magnitude: is the km from the due east point (think 3:00 on a clock), b/c we are 3/4 of the way from due west (9:00), that means we are due north (12:00) so we have to find the distance btw 12:00 and 9:00, which is the same as the hypotenuse btw two radii) so solve for (m = sqrt (r)^2 + (r)^2) b2) direction: is the angle N of E in the 3:00 corner of triangle we made for magnitude, so you would solve with tan^-1 (radius/radius) solve tan inverse of 1 which is 45*

A bicyclist makes a trip that consists of three parts, each in the same direction (due north) along a straight road. During the first part, she rides for -- minutes at an average speed of -- m/s. During the second part, she rides for -- minutes at an average speed of -- m/s. Finally, during the third part, she rides for 8 minutes at an average speed of -- m/s.

a) to find total distance, we have to multiply each of the speeds by their corresponding times (which are in minutes, translate to seconds) and add them together b) to find average velocity multiply each velocity by the corresponding minutes/total minutes and add them all together to find the average velocity (do this b/c they aren't all in equal portions so you can't add them together and divide by three)

A bus makes a trip according to the position-time graph shown in the drawing. What is the average velocity (magnitude and direction) of the bus during each of the segments A, B, and C? Express your answers in km/h. The scale for the time axis is -- h per increment, and scale for the velocity axis is --- km per increment. (Indicate direction by the sign of the velocity.)

so because this graph is asking for both magnitude and direction make sure you put the sign (if negative) in the answer, after that just measure the number of segments and multiply times the scale, then divide change in km by the change in h to get km/h

Four objects move with constant acceleration. Rank the motion diagrams in order of the magnitude of the acceleration, from greatest to least. The time interval between dots is the same in each diagram. (Use only ">" or "=" symbols. Do not include any parentheses around the letters or symbols.)

so look at each of the series of dots to see which ones are accelerating and which are just moving at a constant speed. If the there is the same amount of space between each dot then it has a constant velocity but no acceleration, once you find those, look at the series of dots that have increasing amounts of space between them. When ordering these, put the series with the largest difference in increasing space first, followed by the series with a smaller acceleration, etc. then by the stagnant accelerations. If there are more than one stagnant accelerations then they equal each other.

In getting ready to slam-dunk the ball, a basketball player starts from rest and sprints to a speed of -- m/s in -- s. Assuming that the player accelerates uniformly, determine the distance he runs

so to do this you need to make a graph of velocity vs. time, and then multiply the change in velocity by change in time and then divide by two (to get the area underneath the slope)

A ball is thrown vertically upward, which is the positive direction. A little later it returns to its point of release. The ball is in the air for a total time of t s. What is its initial velocity? Neglect air resistance. (Indicate the direction with the sign of your answer.)

so we're doing something similar to the last problem, which means that we have to find initial velocity with a sign. Because its not a freefall, the initial velocity is positive. We also know that the time traveled up is the same as down so we can divide the time (t) by 2, then we can find the initial velocity by backtracking the same way we did in 7a, so multiply the seconds by 9.8 m/s (gravity) to find the initial velocity (t)/2 * 9.8 m/s

A snowmobile moves according to the velocity-time graph shown in the drawing. What is the snowmobile's average acceleration during each of the segments A, B, and C? The scale for the time axis is -- s per increment, and the scale for the velocity axis is -- m/s per increment.

to find the average acceleration (m/s^2) you have to take the change in velocity and divide by the change in time, so look at each of the scales and multiply accordingly, also for "c" the line isn't perfectly on scale so try estimating the change in time and solving for that