The speed limit on a particular freeway is 28.0 m/s (about 101 km/hour). A car that is merging onto the freeway is capable of accelerating at 5.50 m/s2. If the car is currently traveling forward at 13.0 m/s, what is the shortest amount of time it could take the vehicle to reach the speed limit?
thats not the right answer
To calculate the shortest amount of time it would take for the car to reach the speed limit, we can use the formula:
time = (final velocity - initial velocity) / acceleration
Given:
Initial velocity (u) = 13.0 m/s
Final velocity (v) = 28.0 m/s
Acceleration (a) = 5.50 m/s^2
Plugging in the given values into the formula, we get:
time = (28.0 - 13.0) / 5.50
Calculating the numerator first:
time = 15.0 / 5.50
This gives us:
time = 2.727 seconds
Therefore, the shortest amount of time it could take for the vehicle to reach the speed limit is approximately 2.727 seconds.
To find the shortest amount of time it takes for the car to reach the speed limit, we can use the kinematic equation:
v = u + at
Where:
v = final velocity (speed limit) = 28.0 m/s
u = initial velocity (current speed of the car) = 13.0 m/s
a = acceleration = 5.50 m/s^2
t = time
Rearranging the equation to solve for time (t), we have:
t = (v - u) / a
Substituting the given values, we get:
t = (28.0 - 13.0) / 5.50
Calculating this, we have:
t = 15.0 / 5.50
t ≈ 2.73 seconds
Therefore, the shortest amount of time it could take for the car to reach the speed limit is approximately 2.73 seconds.
t = (Vf - Vo) / a,
t = (28 - 13) / 5.5 = 2.73s.