A remote-controlled car drives from x₀ = +4 m to x = -8 m. Enter the displacement Δx in meters, including the sign.
A lab cart rolls along a straight track toward a motion sensor at the origin. At 1 s the cart is 4 m in front of the sensor, at x = +4 m. At 4 s it has rolled past, 2 m behind it, at x = −2 m. How fast is the cart moving, and which way? Both answers sit in those two logged points.
You've already seen that the slope of a position-time graph at a moment is the velocity at that moment, sign included. On a straight segment the slope is the same everywhere. So calculating the slope once gives the velocity for the whole segment.
To calculate it, pick two points where the line meets gridline crossings. Here, (1 s, +4 m) and (4 s, −2 m). The rise is the change in position, Δx: the later position minus the earlier one, sign included. The run is the time between the two points, Δt.
How fast is the cart moving, and which way?
Write down the values read from the graph:
at 1 s, x = +4 m; at 4 s, x = −2 m
Δx = −2 − 4 = −6 m
Δt = 4 − 1 = 3 s
Write down the equation:
v = Δx/Δt
Substitute in the values:
v = −6 / 3
Simplify:
v = −2 m/s. The cart loses 2 m each second, moving in the negative direction.
With Δx in meters and Δt in seconds, v comes out in m/s. The same rise over run works on any straight position-time segment.
The graph shows a sailboat's position. What is the sailboat's velocity, in m/s, during the straight segment from t = 1 s to t = 5 s?
The graph shows a rowboat's position. What is the rowboat's velocity during the straight segment from t = 2 s to t = 6 s?
Write down the values read from the graph:
at 2 s, x = −3 m; at 6 s, x = +5 m
Δx = 5 − (−3) = 8 m
Δt = 6 − 2 = 4 s
Write down the equation:
v = Δx/Δt
Substitute in the values:
v = 8 / 4
Simplify:
v = +2 m/s
The graph shows a diver's position relative to the surface. What is the diver's velocity, in m/s, during the straight segment from t = 2 s to t = 8 s?
The graph shows a cable car's position. What is its velocity on the straight segment from t = 2 s to t = 8 s?
Write down the values read from the graph:
at 2 s, x = +9 m; at 8 s, x = −9 m
Δx = −9 − 9 = −18 m
Δt = 8 − 2 = 6 s
Write down the equation:
v = Δx/Δt
Substitute in the values:
v = −18 / 6
Simplify:
v = −3 m/s
The graph shows a warehouse robot's position. What is the robot's velocity, in m/s, during the straight segment from t = 1 s to t = 5 s?
The graph shows a maintenance cart's position. What is the cart's velocity, in m/s, during the straight segment from t = 3 s to t = 7 s?
The graph shows a canoe's position. What is the canoe's velocity, in m/s, during the straight segment from t = 1 s to t = 5 s?
The graph shows one journey with two straight segments, P and Q. Which segment shows the greater speed?