The head of a rattlesnake can accelerate 50 m/s2 in striking a victim. If a car could do as well, how long would it take to reach a speed of 78 km/h from rest?
78 km/h
= 780000/3600 m/s
= 21.667 m/s
From initial speed u=0, with acceleration a=50 m/s/s, final speed v=21.667 is attained in t seconds, where
v=ut+(1/2)at²
Can you find t?
Note: it will be less than a second!
To find the time it takes for a car to reach a speed of 78 km/h from rest, we need to convert the speed to m/s and then use the equation:
v = u + at
where:
- v is the final velocity (78 km/h or 21.67 m/s)
- u is the initial velocity (0 m/s)
- a is the acceleration (50 m/s^2)
- t is the time we want to find
First, we convert 78 km/h to m/s:
78 km/h * (1000 m / 1 km) * (1 h / 3600 s) = 21.67 m/s
Now we can substitute the values into the equation:
21.67 m/s = 0 m/s + 50 m/s^2 * t
Simplifying the equation:
21.67 m/s = 50 m/s^2 * t
Divide both sides of the equation by 50 m/s^2:
21.27 m/s / 50 m/s^2 = t
t = 0.4334 seconds (rounded to four decimal places)
Therefore, it would take approximately 0.4334 seconds for the car to reach a speed of 78 km/h from rest if it could accelerate at the same rate as the head of a rattlesnake.
To calculate the time it takes for the car to reach a speed of 78 km/h from rest, we can use the formula for acceleration:
acceleration = (final velocity - initial velocity) / time
We know that the car starts from rest (initial velocity = 0), and we want to find the time it takes to reach a final velocity of 78 km/h.
First, let's convert the final velocity from km/h to m/s for consistency:
Final velocity = 78 km/h = (78 * 1000) m / (60 * 60) s = 21.67 m/s
Now, we have the final velocity (21.67 m/s), initial velocity (0 m/s), and the acceleration (50 m/s^2).
Plugging these values into the formula:
50 m/s^2 = (21.67 m/s - 0 m/s) / time
Simplifying the equation:
50 m/s^2 = 21.67 m/s / time
Now, we can isolate the time variable:
time = 21.67 m/s / 50 m/s^2
Calculating this:
time = 0.4334 seconds
Therefore, it would take approximately 0.4334 seconds for the car to reach a speed of 78 km/h from rest, assuming the same acceleration as the head of a rattlesnake.