a bicyclist is finishing his repair of a flat tire when a friend rides by at 3.5 m/s. two seconds later, the bicyclist hops on his bike and accelerates at 2.4 m/s^2 until he catches his friend? (a) how much time does it take until he catches his friend? (b) how for has he traveled in this time? (c) what is his speed when he catches up?

a. d1 = d2,

3.5(t+2) = 0.5*2.4t^2,
3.5t + 7 = 1.2t^2,
1.2t^2 - 3.5t - 7 = 0,
t = 4.28s.(Use Quadratic Formula).

b. d = d1 = d2 = 3.5(4.28+2) = 22m.

c. V = Vo + at = 0 + 2.4*4.28=10.3m/s.

bruv its spelled physics

(a) It takes him approximately 1.6666666.... seconds to catch his friend. Let's just call it 1.67 seconds because I don't want any fractions causing confusion. Plus, decimals are more fun than fractions, don't you think?

(b) In this time, he has traveled about 4.01 meters. Wow, that's like the distance between you and the fridge when you're craving ice cream!

(c) When he catches up, his speed will be approximately 7.98 m/s. That's fast enough to make his friend wonder if he secretly swapped his bicycle for a rocket! 🚀

To solve this problem, we can use the equations of motion. Let's break it down step by step:

(a) To find the time it takes for the bicyclist to catch his friend, we need to determine the time it takes for the bicyclist to accelerate to the same speed as his friend.
We can use the equation of motion V = U + at, where:
V = final velocity (friend's speed) = 3.5 m/s
U = initial velocity (bicyclist's speed) = 0 m/s (since he was stationary)
a = acceleration = 2.4 m/s^2

Using the equation, we have:
V = U + at
3.5 = 0 + 2.4t

Solving for t, we get:
t = 3.5/2.4
t ≈ 1.4583 seconds

Therefore, it takes approximately 1.4583 seconds for the bicyclist to catch his friend.

(b) To find the distance traveled by the bicyclist in this time, we can use the equation of motion:
S = Ut + (1/2)at^2, where S = distance

Since the initial velocity U is 0 m/s and the acceleration is 2.4 m/s^2, we have:
S = (1/2) (2.4) (1.4583)^2
S ≈ 2.3917 meters

Therefore, the bicyclist has traveled approximately 2.3917 meters in this time.

(c) Finally, to find the speed of the bicyclist when he catches up to his friend, we can use the equation of motion V = U + at.

Using the same formula, we have:
V = 0 + 2.4(1.4583)
V ≈ 3.4999 m/s

The speed of the bicyclist when he catches up to his friend is approximately 3.4999 m/s.