A cyclist is at rest at a traffic light. When the light turns green, he begins accelerating at 2.13 m/s2. How many seconds after the light turns green does he reach a cruising speed of 5.05 m/s?
Kevin,
I looked up how to get the solution and came up with the formula v = at as Damon says, with V = velocity, A = Acceleration, and T being time. SO velocity = acceleration x time.
In our problem, we are give velocity and acceleration, with the unknown being time.
5.05 = 2.13t
t= 5.05/2.13
That division yields 2.37089202, or approximately 2.37 seconds.
I hope that's right. I used to be a physics expert but that was almost 30 years ago.
To find the time it takes for the cyclist to reach a cruising speed of 5.05 m/s, we can use the formula for acceleration:
v = u + at
Where:
v = final velocity (cruising speed)
u = initial velocity (0 m/s, since the cyclist is at rest)
a = acceleration (2.13 m/s^2)
t = time
Step 1: Rearrange the formula to solve for time.
v = u + at
t = (v - u) / a
Substitute the given values into the formula:
v = 5.05 m/s
u = 0 m/s
a = 2.13 m/s^2
Step 2: Calculate the time.
t = (5.05 m/s - 0 m/s) / 2.13 m/s^2
t = 5.05 m/s / 2.13 m/s^2
t = 2.376 m/s^2
Therefore, it takes approximately 2.376 seconds for the cyclist to reach a cruising speed of 5.05 m/s after the light turns green.
To find the time it takes for the cyclist to reach a cruising speed of 5.05 m/s, you will need to use the kinematic equation:
v = u + at
where:
v = final velocity (5.05 m/s)
u = initial velocity (0 m/s, as the cyclist is at rest)
a = acceleration (2.13 m/s^2)
t = time
Rearranging the equation to solve for time (t), we have:
t = (v - u) / a
Plugging in the given values, we get:
t = (5.05 m/s - 0 m/s) / 2.13 m/s^2
Simplifying the equation:
t = 5.05 m/s / 2.13 m/s^2
t ≈ 2.37 seconds
Therefore, it takes approximately 2.37 seconds for the cyclist to reach a cruising speed of 5.05 m/s after the light turns green.