Acceleration 7149

The body went through a uniformly accelerated path of 30 m in 10 seconds while its speed increased five times. Find the initial speed and acceleration.

Correct answer:

v =  0.8571 m/s
a =  0.4286 m/s²

Step-by-step explanation:

$$\begin{gathered} s=30\text{m} \\ t=10\text{s} \\ s=vt+0.5\cdot a{t}^2 \\ at=5v \\ s=a{t}^2/5+0.5a{t}^2 \\ a=\frac{s}{t^2/5+0.5\cdot t^2}=\frac{30}{10^2/5+0.5\cdot 10^2}=\frac{3}{7}\doteq 0.4286{\text{m/s}}^2 \\ {v}_2=a\cdot t=\frac{3}{7}\cdot 10=\frac{3\cdot 10}{7}=\frac{30}{7}\doteq 4.2857\text{m/s} \\ v=v_2/5=\frac{30}{7}/5=\frac{30}{7\cdot 5}=\frac{30}{35}=\frac{6}{7}\text{m/s}=0.8571\text{m/s} \end{gathered}$$

$a=\frac{3}{7}=0.4286{\text{m/s}}^2$

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