The first meters of a 100-meter dash are covered in 2 seconds by a sprinter who starts from rest and accelerates with a constant acceleration. The remaining 90 meters are run with the same velocity the sprinter had after 2 seconds.
a. Determine the sprinter's constant acceleration during the first 2 seconds.
b. Determine the sprinter's velocity after 2 seconds have elapsed.
-- I believe the velocity is 5m/s since the question implies that the sprinter ran 10 meters in 2 seconds. This is my first day in physics, and I really don't understand how to complete this question.
No, his average velocity was 5m/s. He started at zero, had constant acceleration, so he had to be at 10m/s at the end (so his average was 5m/s)
No problem! Let's break down the problem step by step.
First, let's tackle part a: determining the sprinter's constant acceleration during the first 2 seconds.
To find the acceleration, we need to use the kinematic equation:
v = u + at
where:
- v is the final velocity
- u is the initial velocity
- a is the acceleration
- t is the time
We are given that the initial velocity (u) is zero since the sprinter starts from rest.
We are also given that the sprinter covers the first 10 meters in 2 seconds. Using the kinematic equation, we can rearrange it to solve for acceleration:
a = (v - u) / t
Plugging in the values:
v = 10 meters
u = 0 meters (since the sprinter starts from rest)
t = 2 seconds
a = (10 - 0) / 2
a = 10 / 2
a = 5 m/s^2
So, the sprinter's constant acceleration during the first 2 seconds is 5 m/s^2.
Now let's move on to part b: determining the sprinter's velocity after 2 seconds have elapsed.
Since we already know the initial velocity (u) is 0 and the acceleration (a) is 5 m/s^2, we can use the kinematic equation again:
v = u + at
Plugging in the values:
u = 0 meters (since the sprinter starts from rest)
a = 5 m/s^2
t = 2 seconds
v = 0 + 5 * 2
v = 0 + 10
v = 10 m/s
So, the sprinter's velocity after 2 seconds is 10 m/s.
I hope this explanation helps you understand how to solve this problem. If you have any more questions, feel free to ask!
Let's solve the problem step by step.
Step 1: Determine the sprinter's constant acceleration during the first 2 seconds.
We can use the kinematic equation:
v = u + at
where:
v = final velocity
u = initial velocity (0 m/s, as the sprinter starts from rest)
a = acceleration
t = time (2 seconds)
Since the sprinter covers the first 10 meters in 2 seconds, we can substitute the values into the equation:
10 m/s = 0 m/s + a * 2 s
Simplifying the equation:
10 m/s = 2a
Divide both sides by 2:
5 m/s² = a
So, the sprinter's constant acceleration during the first 2 seconds is 5 m/s².
Step 2: Determine the sprinter's velocity after 2 seconds have elapsed.
Using the same kinematic equation as before, we can calculate the velocity:
v = u + at
where:
u = 0 m/s (initial velocity)
a = 5 m/s² (constant acceleration)
t = 2 s (time)
Substituting the values:
v = 0 m/s + 5 m/s² * 2 s
Simplifying the equation:
v = 0 m/s + 10 m/s
Therefore, the sprinter's velocity after 2 seconds have elapsed is 10 m/s.