Uniform Acceleration **Follow these best practices!: ● write units on all of your numbers ● solve the equation for the variable that you want first, then plug in the numbers ● when you plug numbers into the equation, include the units with the numbers ● mentallly do the math on the units too, to make sure you end up with the correct unit that you need ● show your work clearly, like you are trying to show someone else how to do the problem ● begin with a quick sketch about the problem, with the given data written on the sketch ● put a box around each answer 1. A race car can accelerate from 0 to 60 mph in 3 seconds. (a) What is the acceleration of the car in m/s2? (use 1 mile = 1.609 km, and show your work on the unit conversion!) (b) What distance does the car travel while it is accelerating to 60 mph? 2. Starting from rest, a speedboat reaches a speed of 3.2 m/s in 2.0 s. (a) What is its acceleration? (b) What is the speed of the boat after an additional time of 3.0 s has elapsed, assuming its acceleration remains the same? (c) How far did the boat travel during these 5 seconds? 3. A ball is thrown straight up with an initial speed of 15 m/s. (a) How long does it take to reach the highest point? (b) What is its speed 1 second after it is thrown? What is its speed 2 seconds after it is thrown? 4. A bike racer is in a 50 km bike race. For the first 40 km, he bikes at a constant speed of 6.7 m/s. (a) How long did it take him to traverse the first 40 km of the race? (b) After he hits the 40 km mark, he starts to get tired. For the rest of the race, he decelerates at a constant rate. By the end of the race he is only going 4.5 m/s. What was his rate of deceleration between 40 & 50 km? (c) When he gets to the 40 km mark, someone starts a stopwatch. When the stopwatch says 15 minutes, how far along is the biker? (how far is he from the start line?) 5. An airplane lands with a speed of 69 m/s. It needs to decelerate down to a speed of 6 m/s, and it decelerates at a rate of 3.15 m/s2. (a) How many seconds will it take to decelerate down to 6 m/s? (b) How long does the runway need to be? 6. A child drops a small stone into a well. The child releases the stone 1 m above ground level. The child hears the stone hit the bottom of the well in 1.8 seconds. Neglecting air resistance, how deep is the well? 7. A car is traveling east on a road at a constant speed of 2.0 m/s. After 5 s, it starts to accelerate at a constant rate of 3 m/s2. (a) Sketch the graph of position vs time for the car between t=0 s and t = 8 s. Calculate the car’s position at t=5 s and at t = 8 s and accurately label the distances on your graph. (b) Sketch the graph of speed vs time for the car between t=0 s and t=8 s. Calculate the speed of the car at t=8 s and accurately label it on your graph. 8. A child rolls a ball up a steep driveway. It gradually slows down as it goes up the driveway, then turns around and rolls back down to the child. Sketch the graphs of position vs. time and speed vs. time for the ball. You don’t need to calculate anything or put numbers on the axes. Answers: 1. 2. 3. 4. 5. 6. 7. 8. (a) 8.9 m/s2 (b) 40.2 m (a) 1.6 m/s2 (b) 8 m/s (c) 20 m (a) 1.5 s (b) 5.2 m/s, -4.6 m/s (a) 100 minutes (b) -0.0012 m/s2 (c) 45.5 km (a) 20 s (b) 750 m 14.9 m Do your best! Do your best!
