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Uniformly Accelerated Particle Model Worksheet 5:

Quantitative Acceleration Problems

1. A poorly tuned car accelerates from rest to a speed of 28 m/s in 20 s.

a. Make a well-labeled diagram of the situation.

b. Make a well-labeled graphical representation of the situation.

c. List given quantities and quantities to find as you determine:

i. What is the average acceleration of the car?

ii. How far does it travel in this time?

i.

ii.

2. At t = 0 s a car has a speed of 30 m/s. After 6 s, its speed is 15 m/s.

a. Make a well-labeled diagram of the situation.

b. Make a well-labeled graphical representation of the situation.

c. List given quantities and quantities to find as you determine:

i. What is the average acceleration of the car?

ii. How far does it travel in this time?

i.

ii.

Notice that we have a new equation for x:


3. A student drops a rock from the top of a 30 meter tall building.

a. Make a well-labeled diagram of the situation.

b. Make a well-labeled graphical representation of the situation.

c. List given quantities and quantities to find as you determine how fast the rock will be traveling just before impact.

This is not a great problem to solve graphically. My method is to make down positive and plot the speed vs. time using g = 10.We now need to find the time where the area of the triangle is 30m.

Looking at the graph, 2.45s is 24.5m/s.

4. A bus initially moving at 20 m/s slows by 4 m/s each second.

a. Make a well-labeled diagram of the situation.

b. Make a well-labeled graphical representation of the situation.

c. List given quantities and quantities to find as you determine:

  1. How much time does it take the bus to stop?
  2. How far does it travel while braking?

First a graph was plotted where I started at 20m/s and subtracted 4m/s each second until I got to zero. It came out to be 5s.

i.

ii.

5. A car whose initial speed is 30 m/s slows uniformly to 10 m/s in 5 seconds.

a. Make a well-labeled diagram of the situation.

b. Make a well-labeled graphical representation of the situation.

c. List given quantities and quantities to find.

i. Determine the acceleration of the car.

ii. Determine the distance the car travels in the 3rd second (from t = 2s to t = 3s).

i.

ii.

One could also use a rectangle and triangle and add areas or notice that the average velocity is 20m/s and make a rectangle of height 20m/s and take its area.

6. A dog runs down his driveway with an initial speed of 5 m/s for 8 s, then uniformly increases his speed to 10 m/s in 5 s.

a. Make a well-labeled diagram of the situation.

b. Make a well-labeled graphical representation of the situation.

c. List given quantities and quantities to find as you determine:

i. What was the dog’s acceleration during the 2nd part of the motion?

ii. How long is the driveway?

i.

ii.

7. A physics student skis down a slope, with a constant acceleration of 2.0 m/s2 for 15 seconds.

a. Make a well-labeled diagram of the situation.

b. Make a well-labeled graphical representation of the situation.

c. List given quantities and quantities to find as you determine the length of the slope.

First I needed to find v so I took the area of an acceleration/time graph. Knowing the starting velocity was zero and the final 30m/s I plotted a velocity/time graph and calculated the area.

8. A mountain goat starts a rock slide and the rocks crash down the slope 100 m in five seconds.

a. Make a well-labeled diagram of the situation.

b. Make a well-labeled graphical representation of the situation.

c. List given quantities and quantities to find as you determine the acceleration of the rocks.

I used the first graph to get the final velocity, knowing the area and the time. I used that final velocity to plot a quantitative graph and took the slope of it. The area of that graph it 100m.

©Physics1–modified from AMTA 20131