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Answer :
To find the displacement of the car, we can use the physics concepts of kinematics. Here's a step-by-step breakdown:
1. Understand the given information:
- The car is initially at rest, so the initial velocity ([tex]\( u \)[/tex]) is 0 m/s.
- The final velocity ([tex]\( v \)[/tex]) is 40 m/s.
- The time ([tex]\( t \)[/tex]) taken to reach this velocity is 8 seconds.
2. Calculate the acceleration:
We can use the formula for acceleration ([tex]\( a \)[/tex]):
[tex]\[
a = \frac{v - u}{t}
\][/tex]
Plugging in the values:
[tex]\[
a = \frac{40 \, \text{m/s} \ - \ 0 \, \text{m/s}}{8 \, \text{s}} = \frac{40}{8} = 5 \, \text{m/s}^2
\][/tex]
3. Calculate the displacement:
We can use the formula for displacement ([tex]\( s \)[/tex]), which is:
[tex]\[
s = ut + \frac{1}{2} a t^2
\][/tex]
Since the initial velocity [tex]\( u \)[/tex] is 0, the equation simplifies to:
[tex]\[
s = \frac{1}{2} \times a \times t^2
\][/tex]
Substitute the known values:
[tex]\[
s = \frac{1}{2} \times 5 \, \text{m/s}^2 \times (8 \, \text{s})^2
\][/tex]
[tex]\[
s = \frac{1}{2} \times 5 \times 64 = \frac{1}{2} \times 320 = 160 \, \text{m}
\][/tex]
Therefore, the displacement of the car is 160 meters.
1. Understand the given information:
- The car is initially at rest, so the initial velocity ([tex]\( u \)[/tex]) is 0 m/s.
- The final velocity ([tex]\( v \)[/tex]) is 40 m/s.
- The time ([tex]\( t \)[/tex]) taken to reach this velocity is 8 seconds.
2. Calculate the acceleration:
We can use the formula for acceleration ([tex]\( a \)[/tex]):
[tex]\[
a = \frac{v - u}{t}
\][/tex]
Plugging in the values:
[tex]\[
a = \frac{40 \, \text{m/s} \ - \ 0 \, \text{m/s}}{8 \, \text{s}} = \frac{40}{8} = 5 \, \text{m/s}^2
\][/tex]
3. Calculate the displacement:
We can use the formula for displacement ([tex]\( s \)[/tex]), which is:
[tex]\[
s = ut + \frac{1}{2} a t^2
\][/tex]
Since the initial velocity [tex]\( u \)[/tex] is 0, the equation simplifies to:
[tex]\[
s = \frac{1}{2} \times a \times t^2
\][/tex]
Substitute the known values:
[tex]\[
s = \frac{1}{2} \times 5 \, \text{m/s}^2 \times (8 \, \text{s})^2
\][/tex]
[tex]\[
s = \frac{1}{2} \times 5 \times 64 = \frac{1}{2} \times 320 = 160 \, \text{m}
\][/tex]
Therefore, the displacement of the car is 160 meters.
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