A particle 2

If the motion of a particle is described by the relation a(t) = 7t³ + 2 m/s², and the initial velocity of the motion is zero when t = 0 and the distance is 2 m, t = 0.5 s. Determine the velocity and displacement when t = 10 s.

Final Answer:

v =  17520 m/s

Step-by-step explanation:

$$\begin{gathered} a(t)=7t^3+2m/s^2 \\ v(0)=0\text{m/s} \\ x(0)=0\text{m} \\ x(0.5)=2\text{m} \\ {t}_2=10\text{s} \\ a(t)=dv(t)/dt \\ integrate: \\ v(t)=7\cdot t^4/4+2\cdot t+c_1 \\ v(0)=7\cdot 0^4/4+2\cdot 0+c_1=0 \\ {c}_1=0 \\ v(t)=1.75\cdot t^4+2\cdot t \\ x(t)=7\cdot \frac{t^5}{4\cdot 5}+2\cdot t^2/2+c_2 \\ v=1.75\cdot t_2^4+2\cdot t_2=1.75\cdot 10^4+2\cdot 10=17520\text{m/s} \end{gathered}$$

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