Engineers are developing new types of guns that might someday be used to launch satellites as if they were bullets. One such gun can give a small object a velocity of 2.5 km/s while moving it through a distance of only 1.7 cm.

(a) What acceleration does the gun give this object?
(b) Over what time interval does the acceleration take place?

(a)

use v²-u²=2aS
where
S=distance
a=acceleration
v=final velocity
u=initial velocity
Solve for a.
Be sure to use consistent units.
(b)
v=u+at
where t=time,
solve for t.

could you please explain which numbers given go to which variables

To find the acceleration and the time interval, we can use the kinematic equation:

v^2 = u^2 + 2as

where:
v = final velocity
u = initial velocity (0 m/s in this case)
a = acceleration
s = distance

Given:
v = 2.5 km/s = 2500 m/s
s = 1.7 cm = 0.017 m

(a) To find the acceleration, rearrange the equation to solve for a:

a = (v^2 - u^2) / (2s)

Substituting the values:

a = (2500^2 - 0^2) / (2 * 0.017)
a = 3.676 * 10^8 m/s^2

Therefore, the gun gives the object an acceleration of 3.676 x 10^8 m/s^2.

(b) To find the time interval, we can use the equation:

v = u + at

Rearranging the equation to solve for t:

t = (v - u) / a

Substituting the values:

t = (2500 - 0) / (3.676 * 10^8)
t = 6.799 * 10^-6 s

Therefore, the acceleration takes place over a time interval of 6.799 x 10^-6 seconds.

To find the acceleration and time interval for the given scenario, we need to use the formulas of motion.

(a) To calculate the acceleration, we can use the equation:

acceleration = change in velocity / time

The velocity change can be calculated by converting the distance traveled into meters and dividing it by the given time. In this case, we need to consider the distance traveled in meters and the velocity change in m/s.

Given:
Distance traveled = 1.7 cm = 0.017 m
Velocity change = 2.5 km/s = 2500 m/s

Using the formula, we can substitute the values:

acceleration = (2500 m/s - 0 m/s) / t

Simplifying, we get:

acceleration = 2500 m/s / t

(b) To find the time interval, we rearrange the formula:

time = change in velocity / acceleration

Using the values given:

time = 2500 m/s / acceleration

The acceleration and time interval can be found by using the given information and substituting the values into the equations we derived.