Given:

Initial velocity
𝑢
=
1

m/s
u=1m/s
Final velocity
𝑣
=
5

m/s
v=5m/s
Displacement
𝑠
=
15

meters
s=15meters
We need to find:

Acceleration
𝑎
a
Time
𝑡
t
Step 1: Find the acceleration using the SUVAT equation:
𝑣
2
=
𝑢
2
+
2
𝑎
𝑠
v
2
=u
2
+2as
Rearranging for acceleration
𝑎
a:

𝑎
=
𝑣
2
−
𝑢
2
2
𝑠
a=
2s
v
2
−u
2

​

Step 2: Find the time using the equation:
𝑣
=
𝑢
+
𝑎
𝑡
v=u+at
Rearranging for time
𝑡
t:

𝑡
=
𝑣
−
𝑢
𝑎
t=
a
v−u
​

Now, I'll calculate the values.

Let's calculate the acceleration and time using the provided equations.

### Step 1: Find the Acceleration

The SUVAT equation is:

\[
v^2 = u^2 + 2as
\]

We rearrange this to solve for acceleration \( a \):

\[
a = \frac{v^2 - u^2}{2s}
\]

Substituting the given values:

\[
v = 5 \text{ m/s}, \quad u = 1 \text{ m/s}, \quad s = 15 \text{ meters}
\]

\[
a = \frac{(5^2) - (1^2)}{2 \times 15} = \frac{25 - 1}{30} = \frac{24}{30} = 0.8 \text{ m/s}^2
\]

### Step 2: Find the Time

The equation for time \( t \) is:

\[
v = u + at
\]

Rearranging for time \( t \):

\[
t = \frac{v - u}{a}
\]

Substituting the values:

\[
t = \frac{5 - 1}{0.8} = \frac{4}{0.8} = 5 \text{ seconds}
\]

### Final Results:
- **Acceleration, \( a = 0.8 \text{ m/s}^2 \)**
- **Time, \( t = 5 \text{ seconds} \)**

Do you want details or have any questions? Here are five related questions to expand your understanding:

1. What happens to the time if the acceleration is doubled?
2. How would you find the initial velocity if the final velocity, acceleration, and time are known?
3. How does the displacement affect the acceleration if initial and final velocities are kept constant?
4. What would be the displacement if the time was 10 seconds instead of 5?
5. How does changing the final velocity affect the acceleration?

**Tip:** Always double-check the units when performing calculations to ensure consistency and accuracy.

Learn how to calculate acceleration and time using the SUVAT equations. Given initial velocity u = 1 m/s, final velocity v = 5 m/s, and displacement s = 15 meters, find acceleration and time step-by-step. Suitable for high school physics students.

Math Problem Statement

Initial velocity 𝑢

m/s u=1m/s Final velocity 𝑣

m/s v=5m/s Displacement 𝑠

Acceleration 𝑎 a Time 𝑡 t Step 1: Find the acceleration using the SUVAT equation: 𝑣 2

𝑎

Step 2: Find the time using the equation: 𝑣

𝑡

Solution

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