Question
If the velocity-time graph is curved (non-linear), the object is moving with _________.
The correct answer is
Non-uniform acceleration
Understanding Velocity-Time Graphs and Acceleration
The relationship between a velocity-time graph and the object's acceleration is determined by the slope of the graph. Acceleration is defined as the rate of change of velocity.
Mathematically, acceleration ($a$) is the slope of the velocity-time ($v$-$t$) graph:
$ a = \frac{\Delta v}{\Delta t} $
Where:
- $ \Delta v $ is the change in velocity
- $ \Delta t $ is the change in time
Analyzing the graph's shape:
- Linear Graph (Straight Line): A straight line on a velocity-time graph indicates a constant slope. This means the acceleration is constant, referred to as uniform acceleration.
- Curved Graph (Non-linear): A curved line on a velocity-time graph signifies that the slope is changing continuously. A changing slope implies that the acceleration is not constant. This is described as non-uniform acceleration.
Since the question specifies a curved (non-linear) velocity-time graph, the object must be moving with changing acceleration.
Therefore, the object is moving with non-uniform acceleration.
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Important Questions from Acceleration
Acceleration is equal to the rate of change of _________.
At uniform speed the acceleration is
At uniform speed the acceleration is
- If the position of a particle X at time $t$ is given by the equation $x(t) = At^3$, where $A$ is a non-zero constant, determine the nature of its acceleration.
- Which of the following mathematical expressions accurately defines the average acceleration, $a$, of an object that changes its velocity from an initial velocity $v_i$ to a final velocity $v_f$ during a time interval $t$?
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