Distance and speed. A car accelerates at a constant rate from 0 mph to 60 mph in 30 sec. a) How

Distance and speed. A car accelerates at a constant rate...

Key Concepts

Acceleration

Acceleration is the rate at which an object’s velocity changes over time. It characterizes how quickly an object speeds up or slows down, and is defined mathematically by the change in velocity divided by the time interval over which the change occurs. In cases of constant acceleration, the increase in speed is uniform over time.

Kinematic Equations of Motion

Kinematic equations describe the relationships among displacement, initial velocity, final velocity, acceleration, and time for objects moving under constant acceleration. They provide tools for solving problems involving how far an object travels or how fast it moves after a given time, using formulas such as v = u + at and d = ut + (1/2)at².

Average Velocity

Average velocity is the total displacement divided by the total time taken. In uniformly accelerated motion starting from rest, the average velocity is half of the final velocity. This concept is essential for calculating the distance traveled over a time interval when an object accelerates uniformly.

Unit Conversion

Unit conversion involves changing measurements from one unit system to another to ensure consistency in calculations. Problems involving speeds, distances, and time often require converting units (for example, from miles per hour to feet per second) so that all quantities are expressed in compatible units for correct application of equations.

Transcript

00:01 We're told that a car is accelerating from zero to 60 miles per hour in 30 seconds at a constant acceleration.

00:07 And so how fast the car is traveling after this 30 seconds is just going to be equal to this 60 miles per hour.

00:14 Since we're told that we accelerate up to 60 miles per hour to constant acceleration, and then we're just going to be going 60 miles per hour after that.

00:22 So this is equal to 60 miles per hour.

00:25 And then for part b, we're going to figure out the distance travel.

00:30 In the first 30 seconds.

00:31 So the first thing that we're going to want to do to figure this out is convert the 60 miles per hour to miles per second.

00:38 So you have 60 miles per hour.

00:42 We're going to multiply by one hour per 60 minutes.

00:47 And then we're going to multiply by one minute per 60 seconds.

00:53 So now these units will cancel.

00:55 These units will cancel and we'll be left with miles per second.

00:58 So this is going to be equal to.

01:00 To 1 over 60.

01:02 This is in miles per second.

01:05 And then what we can do to actually figure out the acceleration is we're going to just multiply by 1 over 30 seconds.

01:12 Since we're told that we're accelerating at a constant acceleration, that means that in every second in the first 30 seconds, we have the same acceleration.

01:20 So we can just divide by 30 seconds to get our acceleration in miles per second.

01:27 So this is equal to 1 over 900.

01:32 Sorry, this is equal to 1 over 1 ,800.

01:38 And this is in miles per second.

01:41 And now we can actually find the distance traveled...

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