Question

The position of a particle moving in a straight line (x-axis) is given by $x=4t^2–3t^5$. The speed of the particle at $t=2$seconds is (x is in metres)

Answer 1

Step1: Given data

The position of the particle is $x=4t^2–3t^5$

Step2: Formula used

The velocity of the object is given by $v=\frac{dx}{dt}\left(\frac{dx}{dt}=changeinpositionovertime\right)$

Step3: Calculating the speed of the particle

The term ‘v’ is defined as the instantaneous velocity, ‘dx’ being the instantaneous change in displacement and ‘dt’ being the very small instant of time.

Differentiating the given equation

$$\begin{gathered} v=\frac{d}{dt}(4t^2-3t^5) \\ v=\frac{d}{dt}4t^2-\frac{d}{dt}3t^5 \\ v=(2\times 4t^{2-1})-(5\times 3t^{5-1}) \\ v=8t-15t^4 \end{gathered}$$

Now, substituting $t=2$s

$$\begin{gathered} v=(8\times 2)-(15\times 2^4) \\ v=-224m/s \end{gathered}$$

Hence, the speed of the particle at $t=2$seconds is $-224m/s$