84. (a) A car moving at 10 m s?¹ accelerates uniformly at 2...

84. (a) A car moving at 10 m s?¹ accelerates uniformly at 2 m s?² until it reaches a speed limit of 25 m s?¹. The car then moves at this speed until it is at a displacement of 500 m from the point when it started accelerating, the point at which the driver notices traffic lights that are turning amber 5 m away. The reaction time of the driver is 0.3 s. (i) Determine the time taken to accelerate to 25 m s?¹. (ii) Find the displacement of the car when it reached the velocity of 25 m s?¹. (iii) Calculate the time the car was moving at 25 m s?¹. (iv) A police officer gave the driver a ticket for driving through red lights. Use calculations to argue for or against the police officer. (b) A ball thrown vertically up from a stretched hand that is 1.5 m above the floor of the balcony takes 3 s to hit the ground. The roof of the balcony is 2.5 m from the floor. The turning point of the projected ball is just before hitting the roof of the balcony. If the ball takes 1 s to reach the turning point, determine: (i) The velocity with which the ball was thrown. (ii) The height of the balcony floor above the ground. (iii) The velocity of the ball when it hit the ground.

Transcript

00:02 So you have a few constant acceleration problems here.

00:07 So we're going to look at our kinematic equations to solve these problems.

00:12 So part a on number five is asking for how long will it take to come to a stop once you start applying the brakes? and then part b is how far away from the bridge was the driver when she noticed the bridge was out.

00:27 So we were given an initial velocity of 25 meters per second.

00:31 The brakes are causing an acceleration that's in the opposite direction of 3 .0 meters per second squared.

00:42 So we'd make that negative.

00:44 The reaction time was one second, and she stops five meters from the bridge.

00:51 All right, so time to come to a stop.

00:53 That one is the easier part here.

00:57 So let's solve for that.

00:58 We don't need to worry about the reaction time because the way it's more than distance, it's from when we fly the brakes.

01:10 So the equation that we can use here is the one where the distance traveled is irrelevant.

01:17 So we're going to use v equals vi plus a t.

01:26 Vf is going to be zero, and vi is 25, and a is going to be negative 3, and t is worth.

01:37 We don't know.

01:39 So if we do a little bit of algebra here, subtract those sides by 25 and then divide by three, we'll get 8 .33.

01:55 So i'm going to round this to two significant figures.

01:59 So 8 .3 seconds, that's the answer to part a.

02:03 Part b is a little bit more entailed.

02:09 So there's two parts to this.

02:11 One part was when they were traveling before she was able to react.

02:18 So the distance for that will call it x sub one, distance of the first part of the journey.

02:25 That one's just going to be the speed equation, speed times the time.

02:32 So that's going to be vi times this time, reaction type.

02:40 So x sub one is going to be 25.

02:43 25 times 1.

02:47 Now, x sub 2 is how long does it take in distance for this, from the moment that the brakes are applied until they stop 5 meters from the bridge? this is the one where we're going to go with x is equal to v -i times t plus 1 count of a -t squared.

03:23 So the initial velocity was 25, and they began to slow down and applying the brakes over a period of 8 .33 seconds.

03:37 So put that in.

03:42 The reason that we're using 8 .33 here is because this is this x of 2 represents the distance travel while the brakes were applied.

03:51 And we solved for that time period in part a.

03:55 The one second was the reaction time.

03:57 That's why we used it for the first little segment.

04:00 One half times negative three times 8 .333 squared.

04:28 I get a distance traveled of 104 .4 meters.

04:41 So it wants us to know or know that there was also that it didn't stop right before the edge of the bridge break, but five meters before.

04:52 So we need to add that too.

04:53 So the final answer is going to be the x1, which is 25, plus another 104 .2 plus the extra 5 that we had from stopping before we got to the bridge.

05:13 So it's going to be 134 meters or 130.

05:23 If we were rounding to two significant figures, we'd do 130.

05:38 All right.

05:39 So now we're on the number six.

05:41 Number six is about, by an object that's being thrown up in the air, and then it's going to land on the ground.

05:49 It was originally thrown from a window that was 3 .6 meters above the ground.

05:54 So the delta y or change in height is going to be negative 3 .6.

06:00 The initial velocity upwards was 2 .8, and the acceleration of due to gravity is negative 9 .8.

06:11 Remember negative science matter, because we have vectors here.

06:17 So let's see what time it's going to take to hit the ground this time.

06:25 A little different problem than the first one, but it is still a constant acceleration equation.

06:31 We just need to find which one will work for us.

06:34 This time we have everything but the final velocity.

06:40 The final velocity at impact is unknown.

06:44 So we can find the time using delta y is equal to v .i times 2.

07:00 Plus one half a t squared.

07:12 So the one that we don't know is t, so we're going to solve for t.

07:17 So negative 3 .6, that's important that we have that negative sign there.

07:24 B i should actually know, it's 2 .8, t plus one half times negative 9 .a times t squared.

07:40 I'm going to rearrange this so that i can set this up for a quadratic formula.

07:48 So just like algebra class, we're going to have a quadratic formula here.

07:53 And unlike algebra class, this is going to be factored.

07:57 So we're going to have to use a quadratic formula.

08:00 So negative 4 .9 plus 2 .8t plus 3 .6.

08:07 So those are our equation to find time.

08:14 So let's use our calculator to find this.

08:19 So our a value is going to be negative 4 .9.

08:29 It's important that our negatives are in there.

08:34 And then our b value is going to be 2 .8...

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