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## Sagot :

So, ** the particle's initial velocity was 7.453 m/s**.

### Introduction

Hi ! Here, I will help you to explain about **the relationship between acceleration ****with**** changes in velocity and time**. To be able to make changes in speed, a certain time interval is needed. __If the detected change in velocity is negative, then the object will experience a deceleration__. However,

__if the speed change detected is positive, then the object will experience an__.

**acceleration****Here is the equation that applies:**

[tex] \boxed{\sf{\bold{a = \frac{v_2 - v_1}{t}}}} [/tex]

**With the following condition :**

- a = acceleration (m/s²)
- [tex] \sf{v_2} [/tex] = final speed of the object (m/s)
- [tex] \sf{v_1} [/tex] = initial speed of the object (m/s)
- t = interval of the time (s)

### Problem Solving

**We know that :**

- [tex] \sf{v_2} [/tex] = final speed of the object = 9.31 m/s
- a = acceleration = 6.19 m/s²
- t = interval of the time = 0.300 s

**What was asked : **

- [tex] \sf{v_1} [/tex] = initial speed of the object = ... m/s

**Step by step :**

[tex] \sf{a = \frac{v_2 - v_1}{t}} [/tex]

[tex] \sf{a \times t = v_2 - v_1} [/tex]

[tex] \sf{6.19 \times 0.3 = 9.31 - v_1} [/tex]

[tex] \sf{6.19 \times 0.3 = 9.31 - v_1} [/tex]

[tex] \sf{9.31 - v_1 = 1.857} [/tex]

[tex] \sf{9.31 = 1.857 + v_1} [/tex]

[tex] \sf{v_1 = 9.31 - 1.857} [/tex]

[tex] \boxed{\sf{v_1 = 7.453 \: m/s}} [/tex]

**Conclusion**

So, the particle's initial velocity was 7.453 m/s.