Question

A particle moves along a line so that its velocity at time ( t ) is ( v(t)=2 t²-128 ) measured in meters per second. Note: Write the exact answer not the decimal approximation

Answer 1

The particle initially moves backward, but as time progresses its speed increases at an increasing rate because its acceleration is a linear function of time.

Step-by-step explanation:

The particle's velocity as a function of time is given by v(t) = 2t2 - 128 measured in meters per second. To understand what this tells us about the movement of the particle, we need to consider the general behavior of the velocity function.

First, note that when t = 0, the velocity of the particle is -128 m/s. This tells us that initially, the particle is moving backward (if we consider positive direction as forward).

Next, we consider the rate at which the speed changes with time, which is given by the derivative of the velocity function. If we differentiate it with respect to time, we will get the acceleration a(t) = 4t. Since this is a linear function, this tells us that the particle's acceleration is continuously increasing without limit as time progresses. Therefore, the particle is speeding up throughout its motion, and its velocity is increasing at an increasing rate.

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