Exciting Physics Problem to Solve!
Are you ready to tackle this physics challenge?
A bike rider pedals with constant acceleration to reach a velocity of 7.8 m/s over a time of 5.7 s. During the period of acceleration, the bike's displacement is 18.75 m. Can you determine what was the initial velocity of the bike?
Let's Uncover the Solution!
The initial velocity of the bike can be calculated using the given information about displacement, final velocity, and time. The answer is -1.22 m/s.
To find the initial velocity, we will use the following equation:
d = 1/2 * (v_i + v_f) * t
Where:
- d is the displacement
- t is the time
- v_i is the initial velocity
- v_f is the final velocity
By substituting the given values (d = 18.75 m, v_f = 7.8 m/s, t = 5.7 s) into the equation, we can solve for v_i:
18.75 = 1/2 * (v_i + 7.8) * 5.7
Solving for v_i:
18.75/5.7 = 1/2 * (v_i + 7.8)
3.29 = 1/2 * (v_i + 7.8)
3.29 * 2 = v_i + 7.8
6.58 = v_i + 7.8
6.58 - 7.8 = v_i
-1.22 m/s = v_i
Therefore, the initial velocity of the bike was -1.22 m/s.