A car accelerates from 0 to 60 miles per hour in 6.5 seconds. Determine the distance traveled in this time and the acceleration. Assume constant acceleration.
Assuming our answer is to be in ft and sec, convert mi/hr to ft/sec
60 mi/hr * 5280ft/mi * hr/3600sec = 88 ft/sec
v = at
88 = 6.5a
a = 13.538 sec
s = 1/2 a t^2 = 1/2 * 13.538 * 6.5^2 = 286 ft
To determine the distance traveled and acceleration, we can use the formulas of motion with constant acceleration.
First, let's determine the acceleration:
Acceleration (a) = (final velocity - initial velocity) / time taken
Here, the initial velocity (u) is 0 miles per hour, the final velocity (v) is 60 miles per hour, and the time taken (t) is 6.5 seconds.
Substituting these values into the equation gives us:
Acceleration (a) = (60 mph - 0 mph) / 6.5 s
Acceleration (a) = 60 mph / 6.5 s
Now, let's calculate the distance traveled:
Distance (s) = (initial velocity * time taken) + (1/2 * acceleration * time taken^2)
Since the initial velocity (u) is 0 mph, the equation simplifies to:
Distance (s) = 1/2 * acceleration * time taken^2
Substituting the values of acceleration (a = 60 mph / 6.5 s) and time taken (t = 6.5 s) gives us:
Distance (s) = 1/2 * (60 mph / 6.5 s) * (6.5 s)^2
Calculating this equation will give us the distance traveled.