An object is moving in the x-direction at 1.3 m/s when it undergoes an acceleration a=0.50j^m/s2.
Question: find its velocity vector after 4.0s. Express your answer as a comma-separated pair of components.
To find the velocity vector after 4.0 seconds, we can use the following equation:
v = u + at
where:
v is the final velocity vector,
u is the initial velocity vector,
a is the acceleration vector,
t is the time.
Given that the object's initial velocity vector is 1.3 m/s in the x-direction, we can represent it as u = 1.3i m/s (since it is only in the x-direction).
The acceleration vector is given as a = 0.50j m/s^2. This means that the acceleration only affects the y-direction, so there is no acceleration in the x-direction (i-component of acceleration is zero).
Now, we substitute the known values into the equation:
v = u + at
Since the acceleration vector does not affect the x-component, the x-component of the final velocity vector will be the same as the x-component of the initial velocity vector:
v_x = u_x = 1.3 m/s
To find the y-component of the final velocity vector, we need to multiply the acceleration vector by the time:
a_y = 0.50j m/s^2
t = 4.0 s
a_y * t = (0.50j m/s^2) * (4.0 s) = 2.0j m/s
Therefore, the y-component of the velocity vector after 4.0 seconds is 2.0 m/s.
Combining the x and y components, the final velocity vector is:
v = 1.3i + 2.0j
So, the answer is (1.3, 2.0) in terms of components.