Question

You decide to ride your bike, starting from rest. You ride your bike down a long hill. You reach the bottom of the hill with a velocity of 27 m/s and traveled a total of 150 meters. How long did it take you to reach the bottom of the hill, and what was your acceleration?

Answer 1

To calculate the time taken and the acceleration, use the kinematic equations for uniformly accelerated motion, substituting the given initial velocity, final velocity, and distance into the equation v² = v₀² + 2ad to solve for acceleration, and then using v = v₀ + at to find time.

Step-by-step explanation:

To determine how long it took to reach the bottom of the hill and what the acceleration was, we can use kinematic equations for uniformly accelerated motion. As per the question, the cyclist starts from rest (initial velocity v0 = 0) and reaches the bottom of the hill with a velocity (v) of 27 m/s over a distance (d) of 150 meters.

The formula to use in this scenario is v2 = v02 + 2ad, where a is the acceleration and d is the distance covered. Substituting the known values, we have 272 = 0 + 2a(150), which can be solved for a.

To find the time t, we can use the equation v = v0 + at. Once we have determined a, we can solve for t.