Question

(a) Describe this motion in words. (i.e. Only words no numbers) (b) Sketch the shape of the position vs. time graph that describes this motion. (c) Determine the change in position from t = 60s to 90s. Annotate the velocity vs. time graph to show visually how the change in position shows up on it. Show your work and use units. (d) Determine the change in position from t = 10s to 30s. Annotate the velocity vs. time graph to show visually how the change in position shows up on it. Show your work and use units. (e) Construct a quantitative position-time graph for the motion. Assume a position of 50m at t = 0. Be sure to accurately number the scale on the position axis. (f) Determine the object's average velocity. Show your work and use units. Add an average velocity line to your position and velocity graphs.

I need help with d,e and f

Answer 1

(d)

During the time interval $t=10\,s$ to $t=30\,s$ , velocity is $v=-4.5\,m/s$ .

Change in position is $x_{30}-x_{10}=(v)(30-10)=(-4.5)(30-10)=-90\,m$ .

(e)

At time $t=0\,s$ , position is $x_0=50\,m$ .

Blue line depicts the position-time graph.

During the time interval $t=0\,s$ to $t=30\,s$ position time equation is $x=x_0-4.5t=50-4.5t$ .

During the time interval $t=30\,s$ to $t=120\,s$ position time equation is $x=x_0-135+3(t-30)=x_0+3t-225$ .

Red line gives position due to average velocity.

(f)

Average velocity is $v_{av}=\frac{\text {displacement}}{\text{time}}=\frac{3*120-175}{120}=1.542\,m/s$