Scenario 1: Cruising Through The Neighborhood A student...

Scenario 1: Cruising Through The Neighborhood A student driver is practicing their skills while driving on residential streets. The following graph shows their velocity as a function of time. Q1) What is the car's displacement during the 50 s illustrated by the graph? A. 200 m C. 360 m B. 280 m D. 400 m Q2) What is the magnitude of the car's acceleration as it comes to a stop? A. 0 m/s² C. 0.40 m/s² B. 0.16 m/s² D. 0.80 m/s² Q3) Like all young drivers, this one has a pair of fuzzy dice hanging from their rearview mirror. Draw a free body diagram for the fuzzy dice as the car is coming to a stop. (Treat the fuzzy dice as a single object hanging from a string.) At what angle from vertical do the dice hang as the driver is coming to a stop?

Transcript

00:01 Hello, in this question we are given a speed versus velocity, sorry, speed versus time curve.

00:07 Okay, and we need to calculate the displacement and the acceleration when it is coming to stop.

00:13 Okay, so the graph is from 0 to 20 seconds, it is increasing at a constant rate that is if this is velocity coordinate, this is time coordinate.

00:25 So 10, 20, 30, 40 and 50.

00:31 So for 0 to 20 seconds it is increasing at a constant rate of such that it becomes 8 at the end of 20 seconds and then it continues for 20 more seconds and then de -excelate in last 10 seconds.

00:47 So as we know that area under the velocity time curve is nothing but our displacement.

00:52 So this would be our displacement.

00:54 So this is 8.

00:56 So area would be what half into 50 plus 20.

01:01 20 into 8 so this would be what 70 into 4 so 280 meters so the displacement would be 280 meters and average acceleration is what exclamation is what change in velocity divided by change in time so velocity changing from 8 to 0 so velocity changes from 8 to 0 that means final minus initial over t final minus t initial 50 minus 40 that means minus of 0 .8 meter per second square but in the question itself it says that it is de -exillating that means there is no use of putting any negative sign over here because it itself says that what is the de -excellation so we need to only report the magnitude so these would be two answers okay now let me see the third part it says that all young diversities this one has a pair of dice hanging from their rear view mirror we need to draw the free -d -diagram of the mirror of the dyes hanging okay so if dies are hanging somewhere over here and along with the card these dies must also be de -accelerating so it would be having a tension in this direction such that a component of tension gives an backward acceleration so that this acceleration is 0 .8 meter per second.

02:29 If you need to calibrate this angle theta, this is mg, this is the tension p.

02:35 So t cos theta would be mass into acceleration and t sine theta would be mass into g.

02:46 So we can calculate the value of 10 theta, 10 theta would be equal to g over a...

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