Question

Take acceleration, starting point and how long you were traveling for to figure out displacement?

Answer 1

Assuming that the Acceleration is constant, you can use the second kinematic equation:

x = x_0 + (v_0 * t) + (a * t^2)/2

We can assume the object is starting from rest, and the initial location is zero. That makes the equation as follows:

x = (a * t^2)/2

Using this we can solve for displacement from acceleration and time alone.

I’ve attached an example:

Answer 2

To find the displacement from a velocity vs. time graph, calculate the area under the graph line within the given time frame. For linearly increasing velocity over a known time period, the displacement is the area of the triangle formed on the graph, which in the example is 75 m.

Step-by-step explanation:

Calculating Displacement from a Velocity vs. Time Graph

To calculate the displacement of an object from a velocity vs. time graph, you must ascertain the object's acceleration and the time over which it has been traveling. Displacement can be determined by finding the area under the velocity vs. time graph, between the graph line and the time axis.

In our example, we are given a graph where the velocity increases linearly from 0 to 10 m/s over a 15-second interval, indicating constant acceleration. The object's net displacement is equivalent to the area of the triangle formed by the velocity line and the time axis:

(1/2) × base × height = (1/2) × 15 s × 10 m/s = 75 m.

Understanding that displacement may differ from distance traveled is crucial. If the motion includes a return trip to the starting point, the displacement could be zero, but the distance would account for the entire journey.