To solve these questions, we need to use the equations of motion for constant acceleration.
a) What was the time of the run? (in seconds)
We can use the equation:
v = u + at
Where:
v = final velocity (600 km/h)
u = initial velocity (0 m/s, since the car starts from rest)
a = acceleration (to be determined)
t = time
First, we need to convert the final velocity from km/h to m/s:
600 km/h × (1000 m/1 km) × (1 h/3600 s) = 166.67 m/s
Now we can rewrite the equation as:
166.67 = 0 + a × t
Since the initial velocity is 0, the equation simplifies to:
166.67 = a × t
To solve for t, we need to find the acceleration a. We can use another equation:
v^2 = u^2 + 2as
Where:
v = final velocity (166.67 m/s)
u = initial velocity (0 m/s)
a = acceleration (to be determined)
s = displacement (370 m)
Rearranging the equation to solve for a, we get:
a = (v^2 - u^2) / (2s)
a = (166.67^2 - 0^2) / (2 × 370)
a = 13888.9 m/s^2
Now we can substitute the acceleration back into the first equation to solve for t:
166.67 = 13888.9 × t
Solving for t:
t = 166.67 / 13888.9
t ≈ 0.012 seconds
Therefore, the time of the run is approximately 0.012 seconds.
b) What is the magnitude of acceleration? (in m/s^2)
We have already calculated the acceleration in part a) as 13888.9 m/s^2. So, the magnitude of acceleration is 13888.9 m/s^2.