how much would a stationary vehicle have to accelerate in order for it to catch up to another vehicle traveling 74 miles per hour in a distance of .5 miles? what would its final speed be?
To calculate the acceleration required for a stationary vehicle to catch up to another vehicle, we need to consider the initial and final velocities, the distance between them, and the time taken.
First, let's convert the distance to a common unit. Since the other vehicle is traveling at 74 miles per hour, we'll convert the distance of 0.5 miles to the same unit.
1 mile = 1.60934 kilometers (approx.)
0.5 miles ≈ 0.5 * 1.60934 kilometers ≈ 0.805 kilometers
Now, let's use the equation of motion:
\(d = \frac{1}{2} \cdot a \cdot t^2 + v_i \cdot t \)
Where:
d = distance between the vehicles (0.805 km)
a = acceleration (unknown)
t = time taken to catch up (unknown)
\(v_i\) = initial velocity of the stationary vehicle (0 km/h)
Since the stationary vehicle's initial velocity is 0 km/h, the equation becomes:
\(d = \frac{1}{2} \cdot a \cdot t^2\)
Substituting the given values:
0.805 km = 0.5a t^2
Now, let's consider the final velocity. To calculate the final speed, we'll use the equation:
\(v_f = v_i + a \cdot t\)
Since the initial velocity \(v_i\) is 0 km/h, the equation simplifies to:
\(v_f = a \cdot t\)
Now, we have two equations:
0.805 km = 0.5a t^2 ----------- (Equation 1)
\(v_f = a \cdot t\) ----------- (Equation 2)
To solve for the acceleration (a) and final velocity (v_f), we need one more piece of information.