As soon as a traffic light turns green, a car speeds up from rest to 50.0 mi/h with constant acceleration 7.50 mi/h-s. In the adjoining bike lane, a cyclist speeds up from rest to 17.0 mi/h with constant acceleration 14.50 mi/h-s. Each vehicle maintains constant velocity after reaching its cruising speed.

Question

As soon as a traffic light turns green, a car speeds up from rest to 50.0 mi/h with constant acceleration 7.50 mi/h-s. In the adjoining bike lane, a cyclist speeds up from rest to 17.0 mi/h with constant acceleration 14.50 mi/h-s. Each vehicle maintains constant velocity after reaching its cruising speed.

Answer 1

is there a question in there somewhere?

Answer 2

To find the time it takes for the car to reach a speed of 50.0 mi/h, we can use the kinematic equation:

v = v0 + at,

where:
v is the final velocity,
v0 is the initial velocity,
a is the acceleration, and
t is the time.

Let's find the time for the car:
v = 50.0 mi/h,
v0 = 0 (as the car starts from rest),
a = 7.50 mi/h-s.

We can rearrange the equation to solve for t:
t = (v - v0) / a.

Substituting the known values, we have:
t = (50.0 mi/h - 0) / 7.50 mi/h-s,
t = 6.67 s.

Therefore, it takes the car approximately 6.67 seconds to reach a speed of 50.0 mi/h.

Similarly, let's find the time for the cyclist:
v = 17.0 mi/h,
v0 = 0 (as the cyclist starts from rest),
a = 14.50 mi/h-s.

Using the same formula:
t = (v - v0) / a,
t = (17.0 mi/h - 0) / 14.50 mi/h-s,
t = 1.17 s.

So, it takes the cyclist approximately 1.17 seconds to reach a speed of 17.0 mi/h in the same lane.

Note: It's important to be aware of the units used in the problem. In this case, all the velocities are in miles per hour (mi/h), and the acceleration is in miles per hour per second (mi/h-s).