Video Transcript
Which color graph represents the path of a particle with uniform acceleration?
We have been given four graphs (A) to (D) that represent the velocity of a particle at time 𝑡. And we are looking for some information about the acceleration of these particles. We know that acceleration is rate of change of velocity. If we define velocity to be 𝑣, then acceleration 𝑎 is the rate of change of 𝑣 such that 𝑎 is equal to d𝑣 by d𝑡. We know that the derivative of a function is simply the slope of the function. And this means that the acceleration of the particle is given by the slope of the velocity–time graph.
Let’s now consider the slope of our four graphs. Graph (B) is a horizontal line which represents a constant velocity equal to six. This means that the slope or gradient of the line is equal to zero. And we can therefore conclude that this particle has an acceleration equal to zero. Graphs (C) and (D) are both straight-line graphs. However, graph (C) has a positive slope and graph (D) a negative slope. We know that if the velocity is increasing over time and the slope is positive, then the particle is accelerating. However, when the slope is negative, the particle is decelerating. This means that graph (C) shows a particle moving with constant acceleration, whereas graph (D) represents constant deceleration. Both of these would be considered uniform as the graph is a straight line.
The final graph we need to consider is graph (A). Since this graph is a curve, we can find the slope at any point by finding the tangent to the graph at that point. We notice that as time increases, the tangents become steeper. And this means that the acceleration of the particle is increasing over time. Since we were looking for the graph that represents a particle moving with uniform acceleration, it is easy to rule out options (A) and (B). And since particle (D) is decelerating, we can also rule out this graph. We can therefore conclude that graph (C) represents the path of a particle with uniform acceleration.
