Use slope and area calculations to answer the following questions.
Consider the velocity-time graph below. Determine the acceleration of the object whose motion is represented by the graph. (If negative, then enter a negative answer.)
Acceleration
m/s/s
Consider the velocity-time graph below.
Determine the acceleration of the object at 2.4 seconds. (If negative, then enter a negative answer.)
Determine the acceleration of the object at 6.5 seconds. (If negative, then enter a negative answer.)
Determine the acceleration of the object at 11.8 seconds. (If negative, then enter a negative answer.)
Use the velocity-time graph to determine the displacement of the object after a time of 4 seconds. Indicate the direction using a + or a - sign.
Displacement
m
A bicyclist speeds up and then maintains a constant speed. The velocity-time graph represents its motion.
Determine the displacement of the object for the first 3 seconds. Indicate the direction using a + or a - sign.
Displacement (0-3 s)
Determine the displacement of the object for the last 3 seconds.
Displacement (3-6 s)
Determine the displacement of the object for the entire 6 seconds.
Displacement (0-6 s)
The velocity-time graph represents an object moving at constant speed, then slowing down, changing directions, and speeding back up.
Determine the displacement of the object during the first 10.0 seconds. Indicate the direction using a + or a - sign.
Displacement (0-10 s)
Determine the displacement of the object during the last 5.0 seconds. Indicate the direction using a + or a - sign.
Displacement (10-15 s)
Determine the total displacement during the entire 15.0 seconds. Indicate the direction using a + or a - sign.
Displacement (0-15 s)
The graph represents an object that enters into a sloped incline with an initial speed of 16.0 m/s (vi). The object accelerates in the – direction at -3.0 m/s/s. Use this information and the graph to answer the following questions.
Determine the time for the object to reach a speed of 0 m/s. That is, determine t1 on the graph.
Time t1
s
Determine the distance that the object travels up the incline from t = 0 s to a time of t1 seconds.
Distance (from 0 to 1 s)
Time t2 represents the time at which the object reaches its initial location at the bottom of the hill. What is the value of t2?
Time t2
Determine the area between the line on the graph and the time axis from t1 to t2.
Area (from t1 to t2)
m/s•s or m
During a Physics lab, a cart is given a rapid push up a lengthy, inclined board to accelerate it to a speed of 8.0 m/s in 2.0 seconds (t1). Once the push ends, the cart slows down with an acceleration of -0.5 m/s/s. The cart changes directions at t2 and then speeds up as it rolls back down the hill, reaching its starting position at a time of t3.
(NOTE: numbers are randomly-generated; so graph is not drawn to scale.)
Determine the distance the cart traveled during the first 2.0 seconds (from 0.0 s to t1).
Distance (from 0 s to t1)
Determine the acceleration value during the first 2.0 seconds (from 0.0 s to t1).
Use the given acceleration value to determine the time at which the change in direction occurs (t2).
Time (t2)
Determine the distance traveled from a time of 2.0 s (t1) to a time of t2.
Distance (from t1 to t2)
Determine the total distance traveled while moving up the inclined plane (from 0.0 seconds to t2).
Distance (from 0 s to t2)
Determine the time t3 at which the cart rolls back to the starting position that it had before being pushed.
Time t3