Scientists are experimenting with a kind of gun that may eventually be used to fire payloads directly into orbit. In one test, this gun accelerates a 1.9-kg projectile from rest to a speed of 5.1 × 103 m/s. The net force accelerating the projectile is 8.6 × 105 N. How much time is required for the projectile to come up to speed?
To find the time required for the projectile to come up to speed, we can use the equation that relates force, mass, and acceleration:
F = ma
Where:
F = net force (8.6 × 105 N)
m = mass of the projectile (1.9 kg)
a = acceleration
We can rearrange the equation to solve for acceleration:
a = F/m
Substituting the given values:
a = (8.6 × 105 N)/(1.9 kg)
a ≈ 4.53 × 105 m/s²
Now, we can use the equation that relates acceleration, initial velocity, final velocity, and time:
v = u + at
Where:
v = final velocity (5.1 × 103 m/s)
u = initial velocity (0 m/s)
a = acceleration (4.53 × 105 m/s²)
t = time
Rearranging the equation to solve for time:
t = (v - u)/a
Substituting the given values:
t = (5.1 × 103 m/s - 0 m/s)/(4.53 × 105 m/s²)
t ≈ 0.0113 seconds
Therefore, the time required for the projectile to come up to speed is approximately 0.0113 seconds.