A sprinter explodes out of the starting block with an...

A sprinter explodes out of the starting block with an acceleration of $+2.3 \mathrm{m} / \mathrm{s}^{2}$ , which she sustains for 1.2 $\mathrm{s}$ . Then, her acceleration drops to zero for the rest of the race. What is her velocity $(\mathrm{a})$ at $t=1.2 \mathrm{s}$ and (b) at the end of the race?

Key Concepts

Uniformly Accelerated Motion

This concept describes motion where an object’s acceleration is constant over a period of time. When acceleration is constant, the equations of motion can be used to relate displacement, velocity, acceleration, and time. It is fundamental in understanding how an object speeds up over a specific duration when beginning from rest or another initial velocity.

Kinematic Equations

These equations provide mathematical relationships between displacement, initial velocity, final velocity, acceleration, and time. They are essential tools in solving problems involving uniformly accelerated motion, such as calculating the velocity at a given time during acceleration or determining the displacement over a specific period.

Constant Velocity Motion

This concept describes the motion of an object when its acceleration is zero, meaning its velocity remains constant. Once the acceleration ceases, the object continues to move with the velocity it had at the end of the acceleration phase, which is a key factor when analyzing motion in multiple phases.

Segmented Motion Analysis

Many real-world motion problems involve different phases, each with distinct characteristics (such as an acceleration phase followed by a constant velocity phase). Understanding how to analyze each segment separately and then combine the results to assess overall motion is crucial for solving complex kinematics problems.

Transcript

00:01 In this problem, we have a sprinter who starts a race very strong and then finishes the race at a constant velocity.

00:09 So our motion is kind of divided into two parts here.

00:12 So let's talk about the first part of the race first, which is the part where she is actively accelerating the whole way.

00:20 Now, in order to solve any kinematic problem, we need to find three of our five variables and then choose the equation that fits the information we're given.

00:28 So the two numbers that are just kind of given to us is that in the first 1 .2 seconds of the race, she is accelerating at a positive 2 .3 meters per second squared.

00:43 Now, like i said before, we are required to have three of these to solve using any of the equations to the right.

00:48 In this case, we're given one of the somewhat tricky numbers that you're expected to understand from the basis of the question.

00:57 So it tells us that this sprinter is starting the race off with this acceleration.

01:02 And at the very start of the race, this sprinter's or velocity would be zero.

01:08 Because at the start of any race, sprinters are always at zero.

01:12 So this idea of someone starting from rest is a common mechanic of these types of problems.

01:18 And it's just a way of telling us one of our variables without just giving us the number.

01:22 Okay.

01:23 Now, the first part, question a, is asking us to find the final velocity that...

Please give Ace some feedback