A bicyclist is traveling at 19.3 km/h when he speeds up with a constant acceleration of 0.67 m/s2. What is his velocity after 5.00 s?
Add a*t to the initial speed.
a = 0.67 m/s^2
t = 5.00 s
You do the calculation.
You will need the initial speed in m/s to get the answer in m/s. Then you can convert back to km/h if necessary.
To find the velocity of the bicyclist after 5.00 seconds, we can use the equation:
vf = vi + at
Where:
vf = final velocity
vi = initial velocity
a = acceleration
t = time
Given:
vi = 19.3 km/h
First, we need to convert the initial velocity to meters per second (m/s).
1 km/h = 1000 m/3600 s = 5/18 m/s
vi = 19.3 km/h * (5/18 m/s) = 5.36 m/s
Given:
a = 0.67 m/s^2
t = 5.00 s
Now, we can substitute the values into the equation:
vf = 5.36 m/s + (0.67 m/s^2) * 5.00 s
Solving the equation:
vf = 5.36 m/s + 3.35 m/s
vf = 8.71 m/s
Therefore, the cyclist's velocity after 5.00 seconds is 8.71 m/s.
To find the final velocity of the bicyclist after 5.00 seconds, we can use the equation for motion with constant acceleration:
vf = vi + at
Where:
- vf is the final velocity
- vi is the initial velocity
- a is the acceleration
- t is the time
Given:
- vi = 19.3 km/h
- a = 0.67 m/s^2
- t = 5.00 s
First, we need to convert the initial velocity from km/h to m/s because the acceleration is given in meters per second squared.
1 km/h = 1000 m/3600 s = 10/36 m/s
So, the initial velocity (vi) becomes:
vi = 19.3 km/h x (10/36 m/s) = 19.3 x 10/36 m/s = 5.36 m/s (rounded to two decimal places)
Now we can substitute the values into the equation:
vf = 5.36 m/s + (0.67 m/s^2) x (5.00 s)
vf = 5.36 m/s + 3.35 m/s
vf = 8.71 m/s (rounded to two decimal places)
Therefore, the final velocity of the bicyclist after 5.00 seconds is approximately 8.71 m/s.