Question

A motorcycle traveling along a straight road increases its speed from 30.0 ft/s to 50 ft/s in a distance of 180 feet. If the acceleration is constant, how much time elapses while the auto moves this distance?

Answer 1

The time elapsed while the motorcycle moves a distance of 180 ft is 36 seconds.

Step-by-step explanation:

To determine the time elapsed for the motorcycle to travel a distance while accelerating, we can use the equation:

vf = vi + at

where vf is the final velocity, vi is the initial velocity, a is the acceleration, and t is the time elapsed. We are given the initial velocity (vi = 30.0 ft/s),

the final velocity (vf = 50 ft/s),

and the distance (d = 180 ft).

We can calculate the acceleration using the formula:

a = (vf - vi) / t

Substituting the values, we get:

50 ft/s - 30 ft/s = a * t

a = (50 ft/s - 30 ft/s) / t

We can rearrange the equation to solve for t:

t = (50 ft/s - 30 ft/s) / a

t = 20 ft/s / a

Now, we can substitute the distance and solve for time:

180 ft = (1/2) * a * t^2

360 ft = a * t^2

Substituting the expression for t we found earlier:

360 ft = a * (20 ft/s / a)^2

Simplifying the equation, we find:

360 ft = 400 ft/s^2 / a

a = 400 ft/s^2 / 360 ft

a = 10/9 ft/s^2

Now, substituting the value of a, we can solve for t:

t = (20 ft/s) / (10/9 ft/s^2)

t = 20/10 * 9 s

t = 36 s

Therefore, the time elapsed while the motorcycle moves a distance of 180 ft is 36 seconds.