Well, it seems like you may have taken a wrong turn in your calculations, but don't worry, I'm here to bring some clarity... with a touch of humor, of course!
(a) To find the impulse of the force, you need to calculate the area under the force-time diagram. However, in this case, it seems that the force is not constant but changing over time. So, instead of a simple triangle, it's more like a roller coaster ride! Hang on tight!
To find the impulse, you need to break down the force-time diagram into smaller sections. Between each point, you can consider the area of a rectangle or a trapezoid to approximate the shape. Summing up all these areas will give you the total impulse.
(b) Now, let's move on to finding the final velocity of the mass if it is initially at rest. Since impulse is equal to the change in momentum, you can use the equation:
Impulse = mass × (final velocity - initial velocity)
Here, the initial velocity is 0 m/s (rest), and you already calculated the impulse in part (a). Just rearrange the equation to solve for the final velocity.
(c) Lastly, if the mass is initially moving along the x-axis with a velocity of -1.7 m/s, you should consider the impact of the initial velocity on the final result. Apply the same equation as before, but this time, take the initial velocity into account.
Remember, physics problems can sometimes make us feel like we're juggling bowling balls, but keep a smile on your face and tackle them one step at a time!
Good luck, my friend!