While you are sitting on a park bench with your friend, you grab his hat and start running in a straight line away from him. Over the first 49.7m, you accelerate at 1.00m/s^2 up to your maximum running speed. You then continue at you maximum running speed for 7.02s more before your friend catches you. How far from the bench did you get before being caught?\
b). How long did it take for your friend to catch you?
To answer the first question, we need to calculate the distance you traveled before being caught by your friend.
First, let's calculate the time it took for you to reach your maximum running speed. We know that you accelerated at a rate of 1.00 m/s^2 and covered a distance of 49.7m. We can use the equation:
v = u + at,
where v is the final velocity, u is the initial velocity, a is the acceleration, and t is the time taken.
Initially, your velocity was 0 (since you were at rest), and the acceleration is 1.00 m/s^2. Plugging in these values, we can solve for t:
0 + 1.00t = 49.7,
t = 49.7 / 1.00,
t = 49.7s.
So it took you 49.7 seconds to reach your maximum running speed.
Next, we need to calculate the distance covered during the 7.02 seconds of constant maximum running speed. We can use the equation:
d = vt,
where d is the distance, v is the velocity, and t is the time taken.
Since your maximum running speed is constant, we can use the distance formula:
d = 7.02s * v,
where v is the maximum running speed.
Now, let's calculate the distance covered during the constant speed phase. We need to know your maximum running speed, which is not provided in the question. Once you provide that information, we can proceed with the calculations.
For the second question, we need to determine how long it took for your friend to catch you. We can start by calculating the total time it took for your friend to catch up with you. The time is the sum of the time it took for you to reach your maximum running speed (49.7 s) and the additional time during constant speed (7.02 s):
total time = 49.7 s + 7.02 s.
By adding these two values, we can get the total time taken.
Once again, we can proceed with the calculation once you provide your maximum running speed.