Using equations of motion (2 steps numerical)
TLDRIn this instructional video, the speaker tackles two problems involving accelerated motion. The first problem involves a tortoise that uniformly accelerates from rest to 40 meters per second over 100 meters, requiring the calculation of the time taken. The second problem deals with a truck that decelerates uniformly to a stop in five seconds, prompting the calculation of the distance traveled during braking. The instructor emphasizes the importance of using the correct equations of motion for uniformly accelerated or decelerated motion and demonstrates the process of solving for unknown variables like time and displacement.
Takeaways
- π The script discusses solving problems related to accelerated motion, specifically focusing on two scenarios involving a tortoise and a truck.
- π’ The first problem involves a tortoise accelerating uniformly from rest to 40 meters per second over a distance of 100 meters, and the task is to calculate the time taken.
- π The instructor emphasizes that the basic speed equation (speed = distance/time) cannot be used due to the changing nature of speed in accelerated motion.
- π The concept of uniform acceleration is introduced, where acceleration is constant, leading to the use of the equations of motion to solve for unknowns.
- π The equations of motion are presented with variables V (final velocity), U (initial velocity), a (acceleration), t (time), and s (displacement).
- π« The importance of identifying which variables are given and which are unknown in order to select the correct equation of motion is highlighted.
- π’ The instructor demonstrates the process of solving for acceleration first, using the third equation of motion, before calculating time or displacement.
- π The algebraic manipulation to isolate and solve for acceleration (a) is shown, resulting in an acceleration of 8 m/sΒ² for the tortoise.
- β±οΈ Once acceleration is known, the time (t) can be calculated using the first equation of motion, yielding a time of 5 seconds for the tortoise.
- π The second problem involves a truck that decelerates uniformly to a stop in 5 seconds, and the task is to find the distance traveled during braking.
- π The concept of deceleration is explained as negative acceleration, and the truck's deceleration is given as -4 m/sΒ².
- π The process of first calculating the initial velocity (u) using the first equation of motion, and then using either the second or third equation to find the displacement (s), is demonstrated.
- π The final calculation for the truck's displacement during braking is shown to be 50 meters.
Q & A
What is the first problem presented in the script about?
-The first problem is about calculating the time taken for a tortoise to accelerate uniformly from rest to a speed of 40 meters per second, covering a distance of 100 meters.
Why can't we use the formula speed equals distance over time to solve the first problem?
-We can't use this formula because it only works when the speed is constant. In the problem, the tortoise's speed is continuously changing due to acceleration from rest to 40 meters per second.
What does 'uniformly' in the context of the tortoise's acceleration imply?
-'Uniformly' implies that the acceleration is constant, meaning the rate of increase in the tortoise's speed is the same throughout the motion.
What are the three equations of motion mentioned in the script?
-The three equations of motion are: 1) V = U + at, 2) S = Ut + 0.5at^2, and 3) V^2 = U^2 + 2as, where V is the final velocity, U is the initial velocity, a is the acceleration, t is the time, and S is the displacement.
How do we determine which equation to use to find the acceleration (a) in the first problem?
-We use the third equation of motion (V^2 = U^2 + 2as) because it does not include time (t), which is unknown, and we have the values for final velocity (V), initial velocity (U), and displacement (S).
What is the acceleration of the tortoise calculated to be in the first problem?
-The acceleration of the tortoise is calculated to be 8 meters per second squared.
Once the acceleration is known, how do we find the time (t) taken by the tortoise to cover the distance?
-With the acceleration known, we can use either the first or second equation of motion, substituting the known values for final velocity (V), initial velocity (U), acceleration (a), and solving for time (t).
What is the time (t) taken by the tortoise to cover the 100 meters distance?
-The time taken by the tortoise to cover the 100 meters distance is 5 seconds.
What is the second problem presented in the script about?
-The second problem is about calculating the distance traveled by a truck while it decelerates uniformly at 4 meters per second squared and comes to a stop in 5 seconds.
How do we determine the initial velocity (u) of the truck in the second problem?
-We determine the initial velocity (u) of the truck using the first equation of motion (V = U + at), knowing the final velocity (V) is zero, the acceleration (a) is -4 meters per second squared, and the time (t) is 5 seconds.
What is the distance traveled by the truck while braking in the second problem?
-The distance traveled by the truck while braking is 50 meters.
Why can't we use the formula speed equals distance over time for accelerated or decelerated motions?
-We can't use this formula for accelerated or decelerated motions because the speed is continuously changing, and thus we cannot assign a single value for speed over the entire motion.
How can we approach solving problems involving accelerated or decelerated motions?
-We should use the three equations of motion, determine what is given and what is asked, and then choose the appropriate equation to solve for the unknown variable.
Outlines
π’ Calculating Time for Uniformly Accelerated Motion
The first paragraph introduces a physics problem involving a tortoise that accelerates uniformly from rest to a velocity of 40 meters per second, covering a distance of 100 meters. The main goal is to calculate the time taken to cover this distance. The instructor emphasizes that traditional speed formulas cannot be used due to the changing velocity and instead introduces the concept of uniformly accelerated motion, which is characterized by a constant acceleration. The key equations of motion are mentioned, and the instructor guides the viewer to identify which variables are known and which equation to use to solve for time. It is determined that acceleration must be calculated first, using the third equation of motion, which relates final velocity, initial velocity, acceleration, and displacement.
π Solving for Acceleration in Uniform Motion
In this paragraph, the process of calculating the acceleration of the tortoise is detailed. The instructor uses the third equation of motion, rearranges it algebraically to solve for acceleration, and substitutes the known values of final velocity (40 m/s) and displacement (100 m). The units are carefully considered to ensure the correct unit for acceleration (meters per second squared). The algebraic manipulation involves dividing both sides of the equation by two and then by the displacement to isolate acceleration, resulting in an acceleration of 8 m/sΒ². With the acceleration known, the instructor then suggests using one of the other equations of motion to find the time taken for the tortoise to cover the distance, highlighting the importance of choosing the correct equation based on the given variables.
π Deceleration Calculation for a Moving Truck
The third paragraph presents a second problem involving a moving truck that decelerates uniformly to a stop in five seconds with a deceleration of four meters per second squared. The task is to calculate the distance traveled during braking. The instructor explains the concept of deceleration as negative acceleration when the velocity decreases. Given the deceleration, time, and final velocity (which is zero as the truck stops), the initial velocity must be calculated first. The first equation of motion is used for this purpose, yielding an initial velocity of 20 m/s. With the initial velocity determined, the instructor then discusses the selection of an appropriate equation to calculate the displacement, ultimately finding that the truck traveled 50 meters during braking. The paragraph concludes with a reminder of the importance of using the correct equations of motion when dealing with accelerated or decelerated motions and the inapplicability of the basic speed formula in such scenarios.
Mindmap
Keywords
π‘Accelerated motion
π‘Uniform acceleration
π‘Equations of motion
π‘Initial velocity
π‘Final velocity
π‘Displacement
π‘Acceleration
π‘Deceleration
π‘Time
π‘Algebra
π‘Units
Highlights
Problem-solving approach for accelerated motion with a tortoise accelerating uniformly from rest to 40 m/s over 100 meters.
Understanding that speed equals distance over time formula is not applicable due to the tortoise's changing speed.
Introduction of the three equations of motion for constant acceleration scenarios.
Identification of the need to calculate acceleration first before finding the time taken.
Use of the third equation of motion to calculate acceleration when given initial velocity, final velocity, and displacement.
Algebraic manipulation to isolate and solve for acceleration, resulting in 8 m/sΒ².
Once acceleration is known, choosing the appropriate equation of motion to find the time taken.
Calculation of time taken by dividing the equation involving final velocity, initial velocity, and acceleration by the acceleration value.
Conclusion that the tortoise took five seconds to cover 100 meters.
Transition to a second problem involving a moving truck decelerating uniformly to a stop in five seconds.
Understanding that deceleration is represented as negative acceleration in the equations of motion.
Necessity to calculate the initial velocity of the truck before determining the distance traveled during braking.
Utilization of the first equation of motion to find the initial velocity given final velocity, acceleration, and time.
Determination that the truck's initial velocity was 20 m/s before braking.
Once initial velocity is known, selection of an appropriate equation to calculate the braking distance.
Calculation of the braking distance using the second equation of motion with known values.
Conclusion that the truck traveled 50 meters during the braking process.
Emphasis on the importance of using the correct equations for uniformly accelerated or decelerated motion and not relying on the basic speed formula.
Transcripts
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