While driving her new Camaro at 20.0 m/s down a four-lane highway, Jessica comes up behind a slow-moving dump truck and decides to pass in the left-hand lane.
If Jessica can accelerate at a rate of 5.0 m/s^2, how long will it take for her to reach a speed of 30.0 m/s?
( I need as much detail as possible, I am completely lost please explain)
To go from 20.0 to 30.0 m/s, that is a velocity change of 10.0 m/s.
From the definition of acceleration,
a = (velocity change)/(time required)
In this case you know that a = 5.0 m/s^2, so
time = (10.0 m/s)/(5.0 m/s^2)
= 2.0 seconds
Would it not be the square root of two as you are working with seconds squared?
To find the time it will take for Jessica to reach a speed of 30.0 m/s while accelerating at a rate of 5.0 m/s^2, we can use the kinematic equation:
vf = vi + at
Where:
vf = final velocity (30.0 m/s)
vi = initial velocity (20.0 m/s)
a = acceleration (5.0 m/s^2)
t = time
Now, we need to rearrange the equation to solve for time (t):
t = (vf - vi) / a
Substituting the given values:
t = (30.0 m/s - 20.0 m/s) / 5.0 m/s^2
Simplifying the equation:
t = 10.0 m/s / 5.0 m/s^2
t = 2.0 s
So, it will take Jessica 2.0 seconds to reach a speed of 30.0 m/s while accelerating at a rate of 5.0 m/s^2.
To find the time it will take for Jessica to reach a speed of 30.0 m/s, we can use the equation of motion, which relates acceleration, initial velocity, time, and final velocity. The equation is:
Final velocity (v) = Initial velocity (u) + (acceleration (a) × time (t))
In this case, Jessica's initial velocity is 20.0 m/s, and she wants to reach a final velocity of 30.0 m/s. Her acceleration is 5.0 m/s^2.
We can rearrange the equation to isolate time (t):
t = (v - u) / a
Substituting the known values:
t = (30.0 m/s - 20.0 m/s) / 5.0 m/s^2
Now, we can simplify the equation:
t = 10.0 m/s / 5.0 m/s^2
The unit "m/s" cancels out, leaving us with:
t = 2.0 s
Thus, it will take Jessica 2.0 seconds to reach a speed of 30.0 m/s when accelerating at a rate of 5.0 m/s^2.