an arrow is shot from a crossbow. How long will it take the arrow to accelerate from rest to a speed of 152 m/s if the crossbow can accelerate the arrow at a rate of 1.35 x 10^4
v = Vi + a t
152 = 0 + 1.35 * 10^4 t
but 1.35 * 10^4 = 135 * 10^2
t = (152/135) * 10^-2 = 1.13 * 10^-2
= .0113 seconds
Well, I have to say, that is quite the speedy arrow! Let's calculate how long it takes for it to reach a speed of 152 m/s.
Using the equation for acceleration, which is acceleration equals change in velocity divided by time, we can rearrange it to solve for time. So, time is equal to change in velocity divided by acceleration.
In this case, the change in velocity is 152 m/s, and the acceleration is 1.35 x 10^4 m/s^2. Plugging those numbers in, we get:
Time = 152 m/s / (1.35 x 10^4 m/s^2)
Now, let's simplify that. It looks a bit messy, doesn't it? How about we convert it into scientific notation:
Time = 1.13 x 10^-2 seconds
So, it will take the arrow approximately 0.0113 seconds, or about 11.3 milliseconds, to reach a speed of 152 m/s.
Now, that's one speedy arrow! I hope it doesn't have a need for speed!
To determine how long it will take for the arrow to accelerate from rest to a speed of 152 m/s, we can use the following equation:
v = u + at
Where:
v = final velocity (152 m/s)
u = initial velocity (0 m/s, as the arrow starts from rest)
a = acceleration (1.35 x 10^4 m/s^2)
t = time
Rearranging the equation to solve for time (t), we get:
t = (v - u) / a
Substituting the given values, we have:
t = (152 m/s - 0 m/s) / (1.35 x 10^4 m/s^2)
Simplifying further, we get:
t = 11.26 x 10^(-3) s
Therefore, it will take the arrow approximately 11.26 milliseconds (ms) to accelerate from rest to a speed of 152 m/s.
To find the time it takes for the arrow to accelerate from rest to a speed of 152 m/s, we can use the formula:
v = u + at
where:
v = final velocity of the arrow (152 m/s)
u = initial velocity of the arrow (0 m/s, since it starts from rest)
a = acceleration of the arrow (1.35 x 10^4 m/s^2)
t = time taken to accelerate
We need to rearrange the formula to solve for time (t):
t = (v - u) / a
Now, let's substitute the given values into the formula:
t = (152 m/s - 0 m/s) / (1.35 x 10^4 m/s^2)
t = 152 m/s / (1.35 x 10^4 m/s^2)
Now, let's calculate the value:
t ≈ 0.01126 seconds
Therefore, it will take approximately 0.01126 seconds for the arrow to accelerate from rest to a speed of 152 m/s when the crossbow can accelerate the arrow at a rate of 1.35 x 10^4 m/s^2.