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 6.50 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?
vf=vi+at
solve for t
To calculate the shortest amount of time it could take the car to reach the speed limit, we need to use the basic kinematic equation:
v = u + at
where:
v = final velocity (speed limit)
u = initial velocity (current speed of the car)
a = acceleration
t = time
Given:
Speed limit (v) = 28.0 m/s
Current speed of the car (u) = 13.0 m/s
Acceleration (a) = 6.50 m/s²
Plugging in the given values into the equation, we have:
28.0 m/s = 13.0 m/s + 6.50 m/s² * t
Now, let's solve for the time (t):
28.0 m/s - 13.0 m/s = 6.50 m/s² * t
15.0 m/s = 6.50 m/s² * t
Dividing both sides by 6.50 m/s²:
15.0 m/s / 6.50 m/s² = t
t ≈ 2.31 seconds
Therefore, the shortest amount of time it could take for the car to reach the speed limit is approximately 2.31 seconds.