How to Calculate the Acceleration of a Bike?

Question:

A bike accelerates uniformly from rest to a speed of 7.10m/s over a distance of 35.4 m. How can we determine the acceleration of the bike?

Answer:

The acceleration of the bike is 1.42 m/s^2.

To determine the acceleration of the bike, we can use the equation:

a = (vf - vi) / t

Where a is the acceleration, vf is the final velocity, vi is the initial velocity, and t is the time taken.

In this case, the bike starts from rest, so the initial velocity vi is 0 m/s. The final velocity vf is 7.10 m/s. We are not given the time taken t, but we are given the distance traveled d, which is 35.4 m. We can use the formula:

d = (vi + vf) / 2 * t

to find t. Rearranging the formula, we get:

t = 2 * d / (vi + vf)

Substituting the values, we have:

t = 2 * 35.4 m / (0 m/s + 7.10 m/s)

t = 5 seconds

Now, we can substitute the values of vf, vi, and t into the first equation to find the acceleration a:

a = (7.10 m/s - 0 m/s) / 5 s

a = 1.42 m/s^2