Sitting besides a friend on a park bench, you grab her hat and start running in a straight line away from her. Over the first 15.0, you accelerate at 1 m/s^2 up to your maximum running speed. You then continue at your maximum running speed for 15 s more before your friend catches you. Calculate how far from the bench did you get before being caught and how long did it took your friend to catch up with you.

Question

Sitting besides a friend on a park bench, you grab her hat and start running in a straight line away from her. Over the first 15.0, you accelerate at 1 m/s^2 up to your maximum running speed. You then continue at your maximum running speed for 15 s more before your friend catches you. Calculate how far from the bench did you get before being caught and how long did it took your friend to catch up with you.

Answer 1

s₁=15 m, a=1 m/s²,t₂=15 s

s₁=v²/2a
v=sqrt(2as₁)
v=at₁
t₁=v/a
s₂=vt₂

s= s₁+s₂
t=t₁+t₂

Answer 2

To solve this problem, we can break it down into two parts: the time it takes for you to reach your maximum running speed, and the time it takes for your friend to catch up with you.

Let's start with the first part.

1. Finding the time it takes for you to reach your maximum running speed:
You are accelerating at 1 m/s^2 for the first 15.0 s. We can use the equation of motion: v = u + at, where v is the final velocity, u is the initial velocity, a is the acceleration, and t is the time. In this case, the initial velocity is 0 m/s (since you start from rest), the acceleration is 1 m/s^2, and the time is 15.0 s. Plugging in these values, we can solve for the final velocity:

v = u + at
v = 0 + (1)(15.0)
v = 15.0 m/s

So, your maximum running speed is 15.0 m/s.

2. Finding the distance you traveled at your maximum running speed:
You run at your maximum speed for an additional 15 s. Since your velocity is constant, we can use the equation: s = vt, where s is the distance, v is the velocity, and t is the time. Plugging in the values:

s = vt
s = (15.0)(15)
s = 225.0 m

So, you traveled a distance of 225.0 m at your maximum running speed before being caught by your friend.

Now, let's move on to the second part.

3. Finding the time it took for your friend to catch up with you:
Since your friend is at rest initially, they need to cover the same distance that you traveled in the second part (225.0 m). We have the distance and the velocity (your running speed), so we can use the equation: t = s/v, where t is the time, s is the distance, and v is the velocity. Plugging in the values:

t = s/v
t = 225.0/15.0
t = 15.0 s

So, it took your friend 15.0 s to catch up with you.

In summary, you traveled a distance of 225.0 m before being caught, and it took your friend 15.0 seconds to catch up with you.