A car is initially traveling due north at 24.0 m/s.
A.) find the velocity of the car after 4.00 seconds if it's acceleration is 1.60 m/s2 due north.
B.) find the velocity of the car after 4.00 seconds if it's acceleration is instead 1.95 m/s2 due south.
v = Vi + a t
v = 24 + 1.6(4)
v = 24 - 1.95(4)
30.4 m
16.2 s
To find the velocity of the car after a given time, we can use the equation:
v = u + at,
where:
v = final velocity,
u = initial velocity,
a = acceleration, and
t = time.
A) acceleration = 1.60 m/s^2 due north
Given:
u = 24.0 m/s (initial velocity)
a = 1.60 m/s^2 (acceleration)
t = 4.00 seconds (time)
Substituting these values into the equation, we can find the velocity (v):
v = u + at
v = 24.0 m/s + (1.60 m/s^2)(4.00 s)
v = 24.0 m/s + 6.40 m/s
v = 30.4 m/s
Therefore, the velocity of the car after 4.00 seconds with an acceleration of 1.60 m/s^2 due north is 30.4 m/s due north.
B) acceleration = 1.95 m/s^2 due south
Given:
u = 24.0 m/s (initial velocity)
a = -1.95 m/s^2 (acceleration, negative since it is due south)
t = 4.00 seconds (time)
Again, substituting these values into the equation, we can find the velocity (v):
v = u + at
v = 24.0 m/s + (-1.95 m/s^2)(4.00 s)
v = 24.0 m/s - 7.8 m/s
v = 16.2 m/s
Therefore, the velocity of the car after 4.00 seconds with an acceleration of 1.95 m/s^2 due south is 16.2 m/s due north.
To find the velocity of the car after 4.00 seconds, we can use the kinematic equation:
Final velocity (v) = Initial velocity (u) + (acceleration (a) * time (t))
A.) When the acceleration is 1.60 m/s² due north:
Given:
Initial velocity (u) = 24.0 m/s
Acceleration (a) = 1.60 m/s²
Time (t) = 4.00 seconds
Using the kinematic equation, we can calculate the final velocity (v):
v = u + (a * t)
v = 24.0 m/s + (1.60 m/s² * 4.00 s)
v = 24.0 m/s + 6.40 m/s
v = 30.40 m/s
Therefore, the velocity of the car after 4.00 seconds, with an acceleration of 1.60 m/s² due north, is 30.40 m/s due north.
B.) When the acceleration is 1.95 m/s² due south:
Given:
Initial velocity (u) = 24.0 m/s
Acceleration (a) = -1.95 m/s² (acceleration opposite to the direction of motion is considered negative)
Time (t) = 4.00 seconds
Using the same kinematic equation, we can calculate the final velocity (v):
v = u + (a * t)
v = 24.0 m/s + (-1.95 m/s² * 4.00 s)
v = 24.0 m/s - 7.80 m/s
v = 16.20 m/s
Therefore, the velocity of the car after 4.00 seconds, with an acceleration of -1.95 m/s² due south, is 16.20 m/s due north. Note that although the acceleration is due south, the resulting velocity is still due north because the initial velocity and time are not sufficient to reverse the direction.