A vehicle starts from rest and reaches 80 km/h in 12 seconds. How far does it travel in the first 12 seconds?

To determine the distance traveled by a vehicle that starts from rest and accelerates to a certain speed over a specific time, we can use the formula for distance in uniformly accelerated motion. Since the vehicle starts from rest (initial velocity, u = 0), we can use the equation:

Distance (s) = u * t + (1/2) * a * t².

First, we need to calculate the acceleration (a) of the vehicle. The final velocity (v) is given as 80 km/h. To work with standard units, we convert this speed to meters per second:

80 km/h = (80 * 1000 m) / (3600 s) = 22.22 m/s.

Now, we can use the formula for acceleration, which is:

a = (v - u) / t

= (22.22 m/s - 0) / 12 s

= 22.22 m/s / 12 s

= 1.85 m/s².

Having calculated the acceleration, we can now find the distance traveled during the 12 seconds using the distance formula. Plugging in the values:

s = 0 * 12 + (1/2