Question

An object is traveling 12 m/sec headed 315 degrees. It is deflected, and after 1.8 seconds, it is traveling 16 m/sec toward 240 degrees. Find the average acceleration vector.

A) The initial velocity is 12 m/sec
B) The final velocity is 16 m/sec
C) The average acceleration vector is 4 m/sec²
D) The deflection angle is 75 degrees

Answer 1

The average acceleration vector is 2.22 m/s².

Step-by-step explanation:

To find the average acceleration vector, we need to calculate the change in velocity and divide it by the time interval. The change in velocity is the final velocity minus the initial velocity. In this case, it is 16 m/s - 12 m/s = 4 m/s. The time interval is 1.8 seconds. Therefore, the average acceleration vector is 4 m/s divided by 1.8 seconds, which is approximately 2.22 m/s².

Initial velocity components (Vi):

Vi,x = 12 m/sec × cos(315°)

Vi,y = 12 m/sec × sin(315°)

Final velocity components (Vf):

Vf,x = 16 m/sec × cos(240°)

Vf,y = 16 m/sec × sin(240°)

Change in velocity components (ΔV):

ΔVx = Vf,x - Vi,x

ΔVy = Vf,y - Vi,y

The average acceleration (a) can be calculated as:

ax = ΔVx / t

ay = ΔVy / t

Where t = 1.8 seconds, the given time interval.

Using trigonometry, we can determine the magnitude and direction of the average acceleration from its components.