Howard J. answered • 09/20/19

Principal Mech Engr with 35+ years' on-the-job physics experience

Given **v**(0) = -35**i** m/s, and v(7)=20 m/s heading NW. Now if we look at a cartesian coordinate system, NW is in the second quadrant where horizontal components are negative and vertical components are positive and NW runs along the angle 90°+45°=135° degrees. That means

**v** (7) = 20(cos135**i **+ sin135**j**) = 20(-0.707**i **+ .707**j**) = -14.1**i **+ 14.1**j **m/s

To find the average velocity **V**, we need to add **v**(0) and **v**(7):

**V** = **v**(0) + **v**(7) = (-14.1+35)**I** + 14.1**j** = 20.9**i** + 14.1**j**

The average acceleration **A** is the average velocity over the elapsed time Δt = 7 sec:

**A = V**/Δt** **= (20.9**i** + 14.1**j**) m/sec/7 sec = 3**i** + 2**j **m/sec^{2}

so **│A│= **(3^{2}** + **2^{2})^{1/2} = 3.6 m/sec^{2}

and the angle of **A** is tan^{-1}(2/3) = 33.7°

Solution: 3.6 m/sec^{2} at 33.7°.