To solve this problem, we need to determine the total displacement of a body starting from rest (initial velocity = 0) with an acceleration of 20 cm/s² over a time period of 8 seconds.
We use the kinematic equation for displacement:
[tex]\[ s = ut + \frac{1}{2} a t^2 \][/tex]
where:
- [tex]\( u \)[/tex] is the initial velocity,
- [tex]\( a \)[/tex] is the acceleration,
- [tex]\( t \)[/tex] is the time,
- [tex]\( s \)[/tex] is the displacement.
Given:
- Initial velocity ([tex]\( u \)[/tex]) = 0 cm/s (since the body starts from rest),
- Acceleration ([tex]\( a \)[/tex]) = 20 cm/s²,
- Time ([tex]\( t \)[/tex]) = 8 seconds.
Since the initial velocity [tex]\( u \)[/tex] is 0, the equation simplifies to:
[tex]\[ s = \frac{1}{2} a t^2 \][/tex]
Now, plug in the given values:
[tex]\[ s = \frac{1}{2} \times 20 \, \text{cm/s}^2 \times (8 \, \text{s})^2 \][/tex]
[tex]\[ s = \frac{1}{2} \times 20 \times 64 \][/tex]
[tex]\[ s = 10 \times 64 \][/tex]
[tex]\[ s = 640 \, \text{cm} \][/tex]
The displacement in centimeters is 640 cm. To convert this displacement into meters, since 1 meter = 100 centimeters:
[tex]\[ s = \frac{640 \, \text{cm}}{100} \][/tex]
[tex]\[ s = 6.4 \, \text{m} \][/tex]
So, the total displacement of the body in 8 seconds is:
[tex]\[ 640 \, \text{cm} \quad \text{or} \quad 6.4 \, \text{m} \][/tex]
Given the options:
A. 0.064 m
B. 640 cm
C. 64 cm
D. 64 m
The correct answer is B. 640 cm.
