Calculate the displacement and velocity at times of (a) 0.500 s, (b) 1.00 s, (c) 1.50 s, (d) 2.0

step 1 choose downwards to be positive. This simply means that the acceleration is going to be positive

Calculate the displacement and velocity at times of (a)...

Calculate the displacement and velocity at times of (a) $0.500 \mathrm{s},$ (b) $1.00 \mathrm{s},$ (c) $1.50 \mathrm{s},$ (d) $2.00 \mathrm{s}$, and (e) $2.50 \mathrm{s}$ for a rock thrown straight down with an initial velocity of 14.0 m/s from the Verrazano Narrows Bridge in New York City. The roadway of this bridge is $70.0 \mathrm{m}$ above the water.

Key Concepts

Gravitational Acceleration

Gravitational acceleration is the constant acceleration imposed by Earth's gravity on objects in free fall. It is a critical component in vertical motion problems, as it directly influences both displacement and velocity when an object is thrown or dropped, irrespective of its initial conditions.

Initial Conditions

Initial conditions include the initial position and initial velocity from which an object's motion begins. These parameters are essential in kinematics problems as they set the starting point for applying the equations of motion and accurately predicting subsequent displacement and velocity.

Uniformly Accelerated Motion

This concept describes the type of motion in which an object's acceleration remains constant over time. It forms the basis for using the standard kinematic equations that relate displacement, velocity, acceleration, and time, which are crucial for analyzing the motion of objects under constant gravitational acceleration.

Displacement

Displacement refers to the change in position of an object, taking into account both the initial position and the direction of movement. In the context of uniformly accelerated motion, it is calculated by integrating the velocity over time using equations that combine initial velocity, time elapsed, and constant acceleration.

Velocity

Velocity is a vector quantity that represents the rate at which an object changes its position in a specified direction. For motion with constant acceleration, velocity is determined by adding the product of acceleration and time to the initial velocity, reflecting how speed and direction evolve over time.

Transcript

00:01 Choose downwards to be positive.

00:02 This simply means that the acceleration is going to be positive g and then the initial velocity here in the y direction would be positive 14 .0 meters per second.

00:15 And so we can say that then for part a, the change in displacement in the y direction would be equal to vy initial times t plus one half gt squared and we can solve 14 .0 meters per second.

00:33 Multiplied by 0 .50 seconds plus 1 .5 times 9 .8 meters per second squared, multiplied by 0 .50 seconds quantity squared.

00:49 And we find that delta y is equaling approximately 8 .3 meters.

00:56 And then vy final would be equal to vy initial plus gt.

01:04 This would be equal to 14 .0 meters per second plus 9 .80 meters per second squared.

01:13 And then this would be multiplied by t.

01:18 0 .5 .00 seconds.

01:22 And we find that here, the final velocity in the y direction would be equaling 18 .9 meters per second.

01:33 So these would be our two answers for part a, and we're going to do the exact same calculations for all other parts.

01:41 So for part b, we have delta y, equaling again 14 .0 meters per second.

01:54 Now we have 1 .0 seconds plus 1 .5 times 9 .8 meters per second squared, multiplied by 1 .00 seconds, quantified by 1 .00 seconds, quantified.

02:07 Squared and this is equaling now 18 .9 meters.

02:16 Vy final would be equalling vy initial plus gt...

Please give Ace some feedback