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?

2.73s

To find the shortest amount of time it could take the car to reach the speed limit, we can use the kinematic equation:

v = u + at

Where:
v = final velocity (speed limit)
u = initial velocity (current speed of the car)
a = acceleration
t = time

Rearrange the equation to solve for time (t):

t = (v - u) / a

Given:
v = 28.0 m/s
u = 13.0 m/s
a = 6.50 m/s^2

Substitute the values into the equation:

t = (28.0 m/s - 13.0 m/s) / 6.50 m/s^2

Simplify the equation:

t = 15.0 m/s / 6.50 m/s^2

t ≈ 2.31 seconds

Therefore, the shortest amount of time it could take the car to reach the speed limit is approximately 2.31 seconds.